Tree Stem Form Research Articles

Describing and Modelling Stem Form of Tropical Tree Species with Form Factor: A Comprehensive Review

The concept of tree or stem form has been central to forest research for over a century, playing a vital role in accurately assessing tree growth, volume, and biomass. The form factor is an essential component for expressing the shape of a tree, enabling more accurate volume estimation, which is vital for sustainable forest management and planning. Despite its simplicity, flexibility, and advantages in volume estimation, the form factor has received less attention compared to other measures like taper equations and form quotient. This review summarizes the concept, theories, and measures of stem form, and describes the factors influencing its variation. It focuses on the form factor, exploring its types, parameterization, and models in the context of various tropical species and geographic conditions. The review also discusses the use of the form factor in volume estimation and the issues with using default or generic values. The reviewed studies show that tree stem form and form factor variations are influenced by multiple site, tree, and stand characteristics, including site quality, soil type, climate conditions, tree species, age, crown metrics, genetic factors, stand density, and silviculture. The breast height form factor is the most adopted among the three common types of form factors due to its comparative benefits. Of the five most tested form factor functions for predicting tree form factors, Pollanschütz’s function is generally considered the best. However, its performance is often not significantly different from other models. This review identifies the “Hohenadl” method and mixed-effects modelling as overlooked yet potentially valuable approaches for form factor modelling. Using the form factor, especially by diameter or age classes, can enhance tree volume estimation, surpassing volume equations. However, relying on default or generic form factors can lead to volume and biomass estimation errors of up to 17–35%, underscoring the need to limit variation sources in form factor modelling and application. Further recommendations are provided for improving the statistical techniques involved in developing form factor functions.

Correlaciones, parámetros genéticos y fenotípicos en rasgos cuantitativos y cualitativos de Swietenia macrophylla en Ucayali, Perú

The speed of growth in height of Swietenia macrophylla stands out in terms of resistance to attack by the Hypsipyla grandella borer and the selection of fast-growing families can make commercial plantings viable. The characters height, diameter, number of leaves and stem form of trees from 4 families of S. macrophylla, aged 47.5 months, planted in Ucayali, Peru, were used to investigate the possibility of selecting fast-growing genotypes. The average heritability (h2m) and selective accuracy (Acprog) between families were moderate for total height (Ht: h2m: 0.407; Acprog: 0.638) and commercial height (Hc: h2m: 0.472; Acprog: 0.687), in addition to Hc positively correlating with susceptibility to the drill attack. The stem form showed statistical differences between families and great h2m (0.984) and Acprog (0.921). The genetic (rg) and phenotypic (rf) correlations between traits showed that a selection of individuals with greater heights will generally result in greater growth in diameter, number of leaves and better stem form. The study highlights the importance of selecting families with fast growth in height and straight stems to enable, improve the quality and increase the productivity of commercial plantations with the species.

Mixed linear and non-linear tree volume models with regional parameters to main tree species in Finland

AbstractThe volume models that have been used in Finland for the last 40 years, while generally well thought-out, exhibit an illogical behaviour for small trees. In recent studies, tree stem form was observed to have changed in time and also involve spatial variation attributable to environmental factors. It is yet unclear how the stem taper has actually changed. To overcome these problems, we fitted a completely new set of volume and taper curve models and examined whether this change is attributable to the changes in management and environmental factors rather than to measurement errors in the previously used datasets. For the latter, we added a dataset into the analysis, which was smaller but of higher quality due to the destructive nature of the stem taper measurements. We aim at (1) developing a new non-linear variable form factor volume function that works with trees of all sizes, (2) improving the description of the variation of the stem form in time and space by including temperature sum and soil type as predictors, (3) understanding the changes in the stem form by fitting new taper curve models and (4) improving the statistical properties of the predictions by using mixed model techniques and by addressing the effect of parameter uncertainty. To assess the impact of renewing the models, we (5) predicted the mean volume and its confidence interval with each model for forest inventory data at country level. The results show that the tree stem form has a spatial trend that can be described with the temperature sum. Moreover, the changes in stem form also have a spatial trend, with largest changes in Lapland. The difference is mostly observable in the lowest part of the stem, and it is especially large in the largest pines. We conclude that environmental variables can help to improve national stem taper functions in countries with pronounced environmental gradients.

Measuring tree growth using terrestrial laser scanning

Forests are dynamic ecosystems that are constantly changing. The most common natural reasons for change in forests are the growth and death of trees, as well as the damage occurring to them. Tree growth appears as an increment of its structural dimensions, such as stem diameter, height, and crown volume, which all affect the structure of a tree. Repeated measurements of tree characteristics enable observations of the respective increments indicating tree growth. According to current knowledge, the tree growth process follows the priority theory, where trees aim to achieve sufficient lightning conditions for the tree crown through primary growth, whereas increment in diameter results from the secondary growth. Tree growth is known to have an effect on the carbon sequestration potential of trees as well as on the quality of timber. To improve the understanding of the underlying cause–effect relations driving tree growth, methods to quantify structural changes in trees and forests are needed. The use of terrestrial laser scanning (TLS) has emerged during the recent decade as an effective tool to determine attributes of individual trees. However, the capacity of TLS point cloud-based methods to measure tree growth remains unexplored. This thesis aimed at developing new methods to measure tree growth in boreal forest conditions by utilizing two-date TLS point clouds. The point clouds were also used to investigate how trees allocate their growth and how the stem form of trees develops, to deepen the understanding of tree growth processes under different conditions and over the life cycle of a tree. The capability of the developed methods was examined during a five- to nine-year monitoring period with two separate datasets consisting of 1315 trees in total. Study I demonstrated the feasibility of TLS point clouds for measuring tree growth in boreal forests. In studies II and III, an automated point cloud-based method was further developed and tested for measuring tree growth. The used method could detect trees from two-date point clouds, with the detected trees representing 84.5% of total basal area. In general, statistically significant changes in the examined attributes, such as diameter at breast height, tree height, stem volume, and logwood volume, were detected during the monitoring periods. Tree growth and stem volume allocation seemed to be more similar for trees growing in similar structural conditions. The findings obtained in this thesis demonstrate the capabilities of repeatedly acquired TLS point clouds to be used for measuring the growth of trees and for characterizing the structural changes in forests. This thesis showed that TLS point cloud-based methods can be used for enhancing the knowledge of how trees allocate their growth, and thus help discover the underlying reasons for processes driving changes in forests, which could generate benefits for ecological or silvicultural applications where information on tree growth and forest structural changes is needed.

Revealing Changes in the Stem Form and Volume Allocation in Diverse Boreal Forests Using Two-Date Terrestrial Laser Scanning

Tree growth is a multidimensional process that is affected by several factors. There is a continuous demand for improved information on tree growth and the ecological traits controlling it. This study aims at providing new approaches to improve ecological understanding of tree growth by the means of terrestrial laser scanning (TLS). Changes in tree stem form and stem volume allocation were investigated during a five-year monitoring period. In total, a selection of attributes from 736 trees from 37 sample plots representing different forest structures were extracted from taper curves derived from two-date TLS point clouds. The results of this study showed the capability of point cloud-based methods in detecting changes in the stem form and volume allocation. In addition, the results showed a significant difference between different forest structures in how relative stem volume and logwood volume increased during the monitoring period. Along with contributing to providing more accurate information for monitoring purposes in general, the findings of this study showed the ability and many possibilities of point cloud-based method to characterize changes in living organisms in particular, which further promote the feasibility of using point clouds as an observation method also in ecological studies.

Developing taper equations for planted teak (Tectona grandis L.f.) trees of central lowland Nepal

Foresters rely on taper models to estimate total and merchantable volume for commercial species. While there is an abundance of literature in taper modeling for many softwood and hardwood species, little is known of teak tree stem form. Taper modeling is in early stage for the forestry sector in Nepal. Currently, no publicly available taper equations exist for teak trees in Nepal. Therefore, the main goal of this study was to develop a taper equation for valuable teak trees of lowland Nepal. Destructive sampling was carried out in teak plantations in the Sagarnath Forestry Development Project. Five common taper equations (simple, segmented, and variable exponent types) from the literature as well as one dynamic taper equation were considered as candidate models. Our results showed that the nonlinear dynamic taper equation performed best in terms of fit and cross-validation statistics with least error and bias. This new taper model can be considered as a step forward for hardwood forest management in Nepal. It is expected that this equation will assist forest managers to predict stem volume and diameters to any merchantable limit for teak growing in similar site conditions.

Study on the Characteristics and Influencing Factors of the Single Tree Stem Form of Cunninghamia lanceolata Plantation in Hunan Province

Study on the Characteristics and Influencing Factors of the Single Tree Stem Form of Cunninghamia lanceolata Plantation in Hunan Province

Stem Taper Approximation by Artificial Neural Network and a Regression Set Models

Variation in tree stem form depends on species, age, site conditions, etc. Stem taper models that estimate stem diameter at any height and volume should comply with this complexity. In the paper, we propose new methods taking into account both unbiased estimates and stem variability: (i) an expert model based on an artificial neural network (ANN) and (ii) a statistical model built using a regression tree (REG). We used the variable-exponent taper equation (STE) as a reference for these two models. Input data contain information about 2856 trees representing eight dominant forest-forming tree species in Poland (birch, beech, oak, fir, larch, alder, pine, and spruce). The trees were selected across stands varied in terms of age and site conditions. Based on the data, we built ANN and REG models and calculated both stem taper and tree volumes. The results show that ANN is a universal approach that offers the most precise estimation of stem diameter at a particular stem height for different tree species. The results for alder are an exception. In this case, the REG model performs slightly better than ANN. In terms of volume prediction, the ANN model provides the most accurate predictions for coniferous and beech. In general, flexibility and predictive performance of the ANN are better than REG and reference the STE equation.

Особливості моделювання твірної поверхні стовбурів дуба звичайного

Узагальнено досвід дослідження форми стовбурів дерев, який дав змогу зробити висновок про переваги математичного моделювання твірної поверхні для аналізу збігу стовбурів. На основі дослідного матеріалу, зібраного в дубових насадженнях Придніпровського правобережного Лісостепу на 17 тимчасових пробних площах, проаналізовано залежність форми стовбурів дуба звичайного (Quercus robur L.) від висоти та діаметра на висоті 1,3 м. За допомогою графічного аналізу та t-тесту середніх значень коефіцієнтів форми Шиффеля на 5 %-му рівні значущості виявлено відмінність у формі стовбурів дуба різних груп діаметрів. За розрядами висот статистично значущої різниці, за характером збігу не встановлено. Виконаний аналіз дав змогу обґрунтувати доцільність моделювання збігу стовбурів дуба звичайного незалежно від висоти, але в межах 3-х груп діаметрів: 20-28 см, 32-40 см та 44-64 см. Як моделі твірної поверхні стовбурів апробовано показниково-степеневі математичні рівняння A. Kozak (1988) і R. Newnham (1992). Підбір параметрів рівнянь виконано для вибірки з 171 модельного дерева в середовищі R за допомогою функції nls − нелінійна мінімізація суми квадратів відхилень. Систематична помилка обох рівнянь виявилася близькою до нуля (0,9-1,7 %), що дало змогу прийняти їх для моделювання твірної поверхні стовбурів різної форми для встановлених груп діаметрів. Розроблені моделі дають змогу прогнозувати діаметри стовбурів дуба на будь-якій висоті зі стандартною помилкою 1,5-3,2 см. Все ж аналіз розподілу залишків математичних моделей засвідчив переваги моделі A. Kozak (1988), яку рекомендовано використовувати надалі для моделювання розмірно-якісної структури стовбурів дуба звичайного.

Efeito da idade na forma do fuste de Araucaria angustifolia na região Centro-Sul do Paraná

A evolução da forma do tronco de Araucaria angustifolia (Bertol.) Kuntze foi estudada por meio de funções de afilamento e fatores de forma. Os dados utilizados são objeto de análise de tronco e por filmação de árvores em pé em povoados estabelecidos na região Centro-Sul do Paraná, com uma amostra de 45 árvores. Foram ajustadas quatro funções de afilamento para o conjunto total de dados e para os dados estratificados em classes de idade, sendo construídas como curvas de afilamento para diferentes classes de idade. Foi realizado teste de identidade de modelos para comparar modelos completos com o modelo reduzido. Para avaliar um desenvolvimento dos fatores de forma naturais e artificiais, os mesmos foram calculados para o conjunto de dados em diferentes idades, iniciando aos 5 anos. Uma função de afiliação selecionada para o polinômio de Schöpfer. Foram observadas diferenças significativas entre o modelo reduzido e modelos de modelos, com ligeira vantagem com o uso de equações ajustadas por aulas de idade, além de expressiva na forma do tronco com o aumento da idade, também foi constatada pela estabilização dos valores de Fator de forma aos 22 anos.

A general sectional volume equation for classical geometries of tree stem

This work refers to the classical theory of tree stem form. It shows the derivation of a general sectional volume equation for frustums of solids of revolution generated by the function y2 = pnxn where, pn is a positive constant, and n any positive integer. The cylinder case presents a singular situation because of its sectional volume equation cannot be defined for n = 0 as it is known for the generating function. However, that geometry is implicit as a trivial solution of the derived equation. The known sectional volume equations for frustums of paraboloid, conoid and neiloid are particular cases of that equation for n =1, 2, and 3, respectively. The general sectional volume equation has an unexpected statistical nature. It is given as an arithmetic mean of geometric means The classical theory of tree stem form continue being present in the forest measurement teaching and research. This work could contribute to improve the understanding on that theory.

Evolution of tree stem taper in Pinus taeda stands

ABSTRACT: This study aimed to evaluate the evolution of stem taper of trees in Pinus taedastands using stem analysis data from 126 and 120 trees sampled from established stands in Paraná and Santa Catarina States, respectively. The integer and fractional power polynomial was fitted to estimate diameters inside bark along the stem and was used to construct taper curves by age class. The model identity test was applied to verify the change in stem form of trees. The evolution of natural and artificial form factors in the trees was also analyzed. The curves constructed from the fitted taper functions and form factors showed that the stems become more cylindrical with increasing age; the identity test indicated that, in general, the taper curves statistically differ between themselves. This showed that stratifying the data into age classes for fitting in taper functions can produce more accurate assortment estimates.

A new method for capturing stem taper variation for trees of diverse morphological types

Understanding variation in tree stem form is fundamental to both ecological and economic assessments of forest ecosystem structure and function. Stem taper models (STMs) are widely used to describe tree form, but it can be challenging to apply them to trees with stems that diverge from an idealized norm, often leading to the exclusion of many trees from stem taper studies. Here, new “whole-tree” form type classes are advanced as simple and useful groupings for capturing stem form variation of trees of diverse morphological types and tested with a large tree data set without exclusion criteria. New form type classes explained much more of main stem form variation than knowledge of tree species, while “merchantable” form types explained the most variation between trees and stands. Broad-leaved species were much more likely to have complex stem forms than needle-leaved species, but species “evergreenness” was a very weak predictor of stem form variation when tree- and stand-level form variation was accounted for. A new, generalized framework for stem taper modeling is demonstrated, using both species and merchantable form types to capture tree-level random effects. New form types and the STM approach are relatively easy to apply and should be relatively simple to integrate into any conventional forest inventory system. Overall, the study demonstrates the importance of including and accounting for the diversity of observed stem forms in developing STMs.

Artificial Intelligence Procedures for Tree Taper Estimation within a Complex Vegetation Mosaic in Brazil.

Tree stem form in native tropical forests is very irregular, posing a challenge to establishing taper equations that can accurately predict the diameter at any height along the stem and subsequently merchantable volume. Artificial intelligence approaches can be useful techniques in minimizing estimation errors within complex variations of vegetation. We evaluated the performance of Random Forest® regression tree and Artificial Neural Network procedures in modelling stem taper. Diameters and volume outside bark were compared to a traditional taper-based equation across a tropical Brazilian savanna, a seasonal semi-deciduous forest and a rainforest. Neural network models were found to be more accurate than the traditional taper equation. Random forest showed trends in the residuals from the diameter prediction and provided the least precise and accurate estimations for all forest types. This study provides insights into the superiority of a neural network, which provided advantages regarding the handling of local effects.

Constructing tree stem form from digitized surface measurements by a programming approach within discrete mathematics

The main message of this work is the demonstration of possibility of creation of stem shape from digitized points using integer-programming approach. The points are digitized by magnetic motion tracker which in contrast to the laser scanning allows the reconstruction of complete cross-section of stem even in the “hidden (invisible)” part. Three-dimensional information on tree stem form plays an important role in understanding the structure and strength of a standing tree against the forces of wind, snow, and other natural pressure. It also contributes to precision in volume measurement compared to conventional two-dimensional measurement. We investigate approaches for obtaining three-dimensional information of tree stem form from partially organized surface measurements, acquired using a three-dimensional digitizing device (Polhemus FASTRAK® motion tracking device). We then propose a new programming approach from discrete mathematics to construct tree stem form. Our method is based on an optimal connection of neighbor triangles for surface construction, which is created by locally possible combination of three digitized points on the stem surface. We compare the proposed method to the existing heuristic methods of contour tracing and region growing. Our analysis shows that the proposed method provides a consistent construction of tree stem form, for even stems with extremely irregular structure such as those from bent trees and mangrove trees with unique root spread, while the other methods are incapable for constructing such tree stems.

Stand density and fertilization effects on aboveground allocation patterns and stem form of Pinus sylvestris in young stands

The increasing demand for forest biomass for energy generation could be partially met by growing denser stands and use of fertilizer. Before this is done at large scale, more knowledge of the effects of stand density and fertilization on aboveground allocation patterns and stem form is needed. Therefore, effects of pre-commercial thinning (PCT) to 3000 stems ha−1, an unthinned dense control (C), and PCT combined with two levels of fertilization (100 kg ha−1 of nitrogen applied either during the establishment of the field experiment (F1) or annually (F2)) were examined in 23- to 26-year-old Scots pine (Pinus sylvestris L.) stands six years after the establishment of the field experiment. In total, 114 sample trees were harvested using destructive biomass sampling. The growth allocation and stem form of trees with diameter at breast height (DBH; 1.3 m height) >5.0 cm were not affected by either the PCT or fertilization. Small trees (DBH < 5 cm) in denser, unthinned control plots had more slender stems (lower DBH/height ratios) and allocated less growth to branches and foliage than trees in PCT plots. Fertilization had little effect on the stem form and growth allocation of the smallest trees. Therefore, effects of stem density and fertilization on stem form and growth allocation to foliage were only found for small suppressed trees, and the treatments had very little influence on dominant and codominant trees.

Form of turkey oak tree stems in coppice forests of Fruska Gora

The study of tree stem form-form factors and form quotients, and their dependence, and the relation with other volume elements is a necessary precondition for the construction of volume tables by indirect methods, which are increasingly applied. After determining the magnitudes of the above indicators of tree stem form, this paper studies the correlation between normal form quotients and normal form factor, then the correlation between normal form factor and tree diameter and height, as well as the correlation of normal and artificial form factor.

Dickenzuwachs und Stammform von jungen Bäumen in Abhängigkeit von Entastungsintensitäten | Diameter growth and stem form development of young trees, depending on pruning activity

Over a 4-year investigation period we studied the effects of more or less intense pruning on short-term diameter growth and stem form of trees in avenues and parks. While a low degree of pruning hardly has any effect on diameter growth, a high degree of pruning leads to a loss of diameter growth and cylindricality. A high degree of pruning,directly effects assimilation capacity, thereby reducing foliage area and indirectly disturbs internal physiological processes.

Stem Diameter Growth of Scots Pine Trees after Increased Mechanical Load in the Crown during Dormancy and (or) Growth

A field experiment with a 2 ×2 factorial block design (W xS x) was conducted in northern Sweden where the mechanical loads in the crowns of sixteen 2.5m high Scots pine ( Pinus sylvestrisL.) trees were increased during one winter (W 1, dormant period) and (or) summer (S 1, growth period). Trees treated were loaded with five 2kg bags hung over mid-crown branches close to the stem, i.e. 10kg per tree. After treatment, all trees were left to grow untreated for one additional year. Trees were then cut at ground level and annual ring widths for the last 5 years were measured on stem discs taken at 1, 5, 10, 15, 20, 30 and 50% of tree height. Differences between treatments were analysed with two-way factorial ANOVA. Accumulated treatment response was positive for winter loading (W 1S x) at all levels, and statistically significant at 1, 15 and 20% of tree height. Summer loading (W xS 1) had positive effects at the lowest and middle parts of the stem, and negative in between. No statistically significant two-way interaction (W ×S) was observed. Results support the hypothesis that Scots pine trees can retain information about mechanical forces acting on their stems during winter, and respond to this during the following growth period. The results also suggest that stem form of trees in boreal forests may be strongly affected by winter conditions.