Form factors and volume models for Falcataria moluccana in smallholder plantations, Central Kalimantan, Indonesia

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.

Interest in measuring forest biomass and carbon stock has increased as a result of the United Nations Framework Convention on Climate Change, and sustainable planning of forest resources is therefore essential. Biomass and carbon stock estimates are based on the large area estimates of growing stock volume provided by national forest inventories (NFIs). The estimates for growing stock volume based on the NFIs depend on stem volume estimates of individual trees. Data collection for formulating stem volume and biomass models is challenging, because the amount of data required is considerable, and the fact that the detailed destructive measurements required to provide these data are laborious. Due to natural diversity, sample size for developing allometric models should be rather large. Terrestrial laser scanning (TLS) has proved to be an efficient tool for collecting information on tree stems. Therefore, we investigated how TLS data for deriving stem volume information from single trees should be collected. The broader context of the study was to determine the feasibility of replacing destructive and laborious field measurements, which have been needed for development of empirical stem volume models, with TLS. The aim of the study was to investigate the effect of the TLS data captured at various distance (i.e. corresponding 25%, 50%, 75% and 100% of tree height) on the accuracy of the stem volume derived. In addition, we examined how multiple TLS point cloud data acquired at various distances improved the results. Analysis was carried out with two ways when multiple point clouds were used: individual tree attributes were derived from separate point clouds and the volume was estimated based on these separate values (multiple-scan A), and point clouds were georeferenced as a combined point cloud from which the stem volume was estimated (multiple-scan B). This permitted us to deal with the practical aspects of TLS data collection and data processing for development of stem volume equations in boreal forests. The results indicated that a scanning distance of approximately 25% of tree height would be optimal for stem volume estimation with TLS if a single scan was utilized in boreal forest conditions studied here and scanning resolution employed. Larger distances increased the uncertainty, especially when the scanning distance was greater than approximately 50% of tree height, because the number of successfully measured diameters from the TLS point cloud was not sufficient for estimating the stem volume. When two TLS point clouds were utilized, the accuracy of stem volume estimates was improved: RMSE decreased from 12.4% to 6.8%. When two point clouds were processed separately (i.e. tree attributes were derived from separate point clouds and then combined) more accurate results were obtained; smaller RMSE and relative error were achieved compared to processing point clouds together (i.e. tree attributes were derived from a combined point cloud). TLS data collection and processing for the optimal setup in this study required only one sixth of time that was necessary to obtain the field reference. These results helped to further our knowledge on TLS in estimating stem volume in boreal forests studied here and brought us one step closer in providing best practices how a phase-shift TLS can be utilized in collecting data when developing stem volume models.

Sectional equations and mathematical volume models are a reliable way to estimate carbon sequestration and storage, which is a key foundation for forest management and conservation. The objective of this study was to assess stem volume and form factor through the classical sectional method to then, using five regression models commonly used for forest management, identify the most suitable mathematical model to estimate the stem volume in a commercial forest plantation (CFP) of Pinus pseudostrobus Lindley in the Comunidad Indígena de Nuevo San Juan Parangaricutiro, Michoacán, in Western Mexico. By using 10, 15 and 20 yr.-old sampling points and two sampling methods (destructive and nondestructive), we found a form factor 0.42, 0.48 and 0.51 and stem volume of 0.098 m3, 0.400 m3 and 0.804 m3 for the three ages assessed, which presented diameter classes (DC), from 10 to 45 cm. The mathematical models identified that age of plantation determines stem volume and form factor, and the models that best fit volume estimation were the Schumacher-Hall model and the Australian model with an R2 adj range between 0.89 and 0.99. Estimation of stem volume is of vital importance to assess the income generated by the timber industry, and relevant for forest conservation, management, and carbon sequestration studies.

Devido à carência de modelos simples, robustos e precisos para estimação de volume em Araucaria angustifolia, a despeito de muitos trabalhos já realizados, este estudo objetivou avaliar o emprego do fator de forma por classe diamétrica em comparação com modelos de regressão, visando a estimativa volumétrica de um povoamento de araucária em Quedas do Iguaçu -PR.Para isso, 50 árvores foram cubadas rigorosamente e três técnicas de estimação foram comparadas estatisticamente: fator de forma médio, fatores de forma médios por classes de diâmetro; e equações de regressão.Os fatores de forma individuais variaram de 0,49 a 0,97, com média de 0,59, ao passo que os valores médios por classe variaram de 0,54 a 0,69.O modelo de Spurr logaritmizado apresentou o melhor ajuste entre os sete modelos de regressão testados.Além disso, os fatores médios por classes de diâmetro acarretaram em estimativas volumétricas mais precisas e acuradas entre as três técnicas empregadas, quebrando o paradigma de que as equações volumétricas sempre geram estimativas de melhor qualidade, quando comparadas ao fator de forma.Todavia, a aplicação do fator de forma médio geral resulta em estimativas enviesadas para menos (subestimativas), notadamente para as árvores de maior diâmetro.Com isso, concluiu-se que o uso de fatores de forma por classe de diâmetro é a melhor opção no presente caso.

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.

Societal Impact Statement Trees in the genus Paulownia play a crucial role in sustainable forestry, rural economic development, and carbon mitigation due to their rapid growth, exceptional hardwood properties, and prominent carbon sequestration capacity. This review highlights the societal value of Paulownia trees and synthesizes several potential drivers of extraordinarily fast growth in these trees. These insights are valuable for maximizing Paulownia 's potential for timber production and carbon sequestration, and they also provide a valuable model for studying mechanisms of rapid growth in hardwood trees. Summary Paulownia is a genus of fast‐growing deciduous hardwood trees that are economically and ecologically important. Originally from East Asia, Paulownia are grown globally for their robust timber, agroforestry, and effective carbon dioxide drawdown, services that arise from their remarkably fast growth. Despite their clear value, the underlying drivers of fast growth in this genus remain poorly understood. Here, we review potential causes of fast growth in Paulownia and identify several potential adaptations, including photosynthetic metabolism, non‐foliar photosynthesis, tree habit, leaf structure, and hydraulic investment, that may contribute to fast growth in these trees. Our review highlights the paucity of evidence that would enable evaluation of these properties of Paulownia species and makes recommendations for future research needed to help explain drivers of fast growth in these important trees. In doing so, this review establishes a promising model system to study rapid growth in hardwood trees, their benefits to plantation cultivation, and potential for bioengineering.

Exact knowledge over tree growth is valuable information for decision makers when considering the purposes of sustainable forest management and planning or optimizing the use of timber, for example. Terrestrial laser scanning (TLS) can be used for measuring tree and forest attributes in very high detail. The study aims at characterizing changes in individual tree attributes (e.g., stem volume growth and taper) during a nine year-long study period in boreal forest conditions. TLS-based three-dimensional (3D) point cloud data were used for identifying and quantifying these changes. The results showed that observing changes in stem volume was possible from TLS point cloud data collected at two different time points. The average volume growth of sample trees was 0.226 m3 during the study period, and the mean relative change in stem volume was 65.0%. In addition, the results of a pairwise Student’s t-test gave strong support (p-value 0.0001) that the used method was able to detect tree growth within the nine-year period between 2008–2017. The findings of this study allow the further development of enhanced methods for TLS-based single tree and forest growth modeling and estimation, which can thus improve the accuracy of forest inventories and offer better tools for future decision-making processes.

Ülkemizin ekolojik ve ekonomik açıdan önemli ağaç türlerinden birisi Kızılçam (Pinus brutia Ten.)’dır. Bu nedenle türün sürdürülebilir yönetimi ve planlaması için hasılat ve büyüme modellerine ihtiyaç vardır. Hasılat ve büyüme modellerinin en önemli bileşenlerinden birisi de ağaç hacim tahminleridir. Ülkemizde ağaç hacim tahminleri genellikle tek girişli hacim tabloları kullanılarak yapılmaktadır. Ancak söz konusu hacim tabloları kullanılarak, güvenilir ve doğru hacim tahminleri yapılması oldukça güçtür. Günümüzde ağaç hacim tahminleri için en doğru yaklaşım tarzlarından birinin uyumlu gövde çapı ve gövde hacim denklemleri olduğu ifade edilmektedir. Bu çalışmada, Antalya-Gebiz yöresi doğal kızılçam meşcereleri için uyumlu gövde hacmi ve gövde çapı denklemleri geliştirilmiştir. Bu amaçla, Max ve Burkhart (1976), Parresol vd. (1987), Clark vd. (1991) ve Jiang vd. (2005) tarafından geliştirilen parçalı gövde çapı modelleri seçilmiştir. Seçilen modeller, gövde çapı ve gövde hacim tahminleri açısından tüm ağaç ve gövdenin farklı bölümleri için karşılaştırılmıştır. Geliştirilen tüm modeller gerek gövde çapı gerekse gövde hacim tahminlerinde başarılı sonuçlar üretmiştir. Test edilen tüm modeller, gövde çapı tahminlerindeki varyasyonun %94’ünden; gövde hacim tahminlerindeki varyasyonun ise %95’inden daha fazlasını açıklamıştır. Gövde çapı tahminlerindeki hatalar 2,8 cm’den, gövde hacim tahminlerindeki hatalar ise 0,02 m3’ten daha az bulunmuştur. En başarılı tahminler Clark vd. (1991) tarafından geliştirilen gövde çapı modeli ile elde edilmiştir. Ayrıca çalışma kapsamında geliştirilen modeller, yöresel tek girişli hacim tablosu değerleri ile de karşılaştırılmıştır. Test edilen dört gövde hacim modeli de yöresel tek girişli hacim tablosundan daha iyi sonuçlar ortaya koymuştur.

Introduction Butea monosperma (Lam.) Taub. is an ecologically and economically important dry-deciduous tree species widely distributed in the semi-arid Bundelkhand region. Despite its multipurpose utility, like gum production, flowers for dye, fodder, fuelwood, and medicinal compounds, there is limited scientific information on its growth variation, biomass and carbon dynamics, and nutritional composition across diameter classes and localities. Understanding silvicultural behaviour and biochemical variation is crucial for optimizing its use in agroforestry, carbon sequestration, and livelihood enhancement in the Bundelkhand region. Methods A multistage stratified random sampling approach was adopted across 10 localities (Jhansi and Lalitpur districts), covering agroforestry systems (AFS) and naturally regenerated areas (NRA). The research employed a factorial randomized block design with the first factor as three diameter classes: D 1 (10–30cm), D 2 (30–50cm), and D 3 (>50cm), and the second factor as locality (L 1 –L 5 ). Trees per class per site were measured for DBH, height, stem volume, above- and below-ground biomass, carbon stock, and CO₂ mitigation potential. Reproductive traits (leaf and flower characteristics), gum yield, and biochemical properties of gum and flowers were analysed using standard laboratory procedures. Results Diameter class exerted a significant influence on tree growth, biomass accumulation, and carbon sequestration. The largest diameter class (D 3 ) consistently recorded the highest DBH (55.56cm), stem volume (10.90m), AGB (0.72t tree −1 ), BGB (0.18t tree −1 ), Carbon stock (0.45t tree −1 ), and CO 2 mitigation potential (1.67t tree −1 ) in Jhansi district. Lalitpur district also followed the same trend in terms of growth, biomass, and carbon parameters. Reproductive traits such as leaf fresh/dry weight and flower characteristics showed mostly non-significant differences among diameter classes and localities. Gum yield was significantly highest ( p ≤0.05) in Jhansi and Lalitpur districts in medium-sized trees (D 2 ) (207.76g tree −1 , 224.6g tree −1 ), indicating locality-specific physiological responses. Biochemical composition of gum exhibited significant variation, with higher phenolic content (13.61mgg −1 ), ash (4.12%), and ascorbic acid (42.08mg 100g −1 ) in larger diameter trees. Flower biochemical traits differed significantly across sites, with Lalitpur showing greater variation in phenols (16.03mgg −1 ), ash (6.78%), antioxidants (68.90%), and carotenoids (37.14mg 100g −1 ). Overall, D 2 and D 3 trees demonstrated superior biochemical traits, reflecting higher metabolic activity. Conclusion Butea monosperma shows substantial variation in growth performance, carbon sequestration potential, gum productivity, and biochemical composition across diameter classes and localities in Bundelkhand. Larger trees serve as major contributors to biomass and carbon storage, while gum and biochemical quality are influenced by both tree size and site conditions. The findings highlight that B. monosperma has strong ecological resilience and economic potential, supporting its wider adoption in agroforestry and livelihood-based interventions in semi-arid regions.

The National Forest Inventory in Lithuania has collected Scots pine (Pinus sylvestris) and Norway spruce (Picea abies) trees measurement data across the country. Investigations to determine the suitability of these data for updating stem profile and volume models are required. New models for stem volume and stem profile (taper) were developed using a q-exponential function in the symbolic computational language MAPLE. Work associated with the National Forest Inventory has derived very accurate Scots pine and Norway spruce trees stem profile equations that have an application not only in deriving total tree volume estimates, but as a cost-effective mensuration tool to estimate stem volume at any part of the trunk. Three previously constructed models and a new q-exponential model for stem profile and stem volume were employed to compare predicted values with empirical values of diameter outside bark and stem volume. Performance statistics for the stem volume and stem profile equations included four statistical indices: mean percentage of absolute bias, precision, Acaike’s Information Criteria, and an adjusted coefficient of determination.

The aim of the study was to estimate stem volume and taper models for Pinus kesiya (Royle ex Gordon). The volume function provides a simple prediction model for the stem volume. Taper models were developed for over- and under-bark diameters. The under-bark taper curve was determined with the variable-exponent taper equation, whereas the over-bark taper curve was derived from the predicted under-bark taper model using the variable-exponent form of the bark-thickness model. Because of the spatial correlation structures of the data, the general assumption of uncorrelated residuals did not hold. In addition, the models were assumed to contain random parameters that vary from stand to stand and from tree to tree. Therefore, the fixed and random parameters of the models were estimated with the generalized least squares technique. The results of the study show that the mixed models for stem volume and taper are more reliable volume and diameter predictors for P. kesiya than earlier taper and volume functions.

Long-term effects of superphosphate fertilization on stem form, taper and stem volume estimation of Pinus radiata

Abstract. Rahayu S, Triyogo A, Widyastuti SM, Musyafa’, Ardianyah F. 2021. Pests and diseases on Falcataria moluccana trees in agroforestry systems with pineapple in East Java, Indonesia. Biodiversitas 22: 2779-2788. The agroforestry system using Falcataria moluccana (Sengon) and Ananas comosus (pineapple) is considered as a profitable intercropping system in Indonesia. To make it viable, it is necessary to evaluate the effect of mixed cropping on the incidence and severity of diseases and pests on Sengon trees and apply management measures. The present study was conducted (i) to assess the pest and disease problems on Sengon trees in the agroforestry system and (ii) to identify the most harmful pathogen/pest which affects the growth and causes mortality of Sengon trees at the beginning of intercropping and after the removal of pineapple from the system. Incidence of pests and diseases were assessed in 3 replicate blocks with one-year-old Sengon trees mixed with pineapple, and in another 3 plots with four-year-old Sengon trees from where pineapple was removed after harvesting. Sengon and pineapple were planted in the plots using alley cropping method with 3 x 4 m2 spacing. The results showed that there were no significant pest and disease problems on pineapple. However, Sengon was infested by the white grub Lepidiota stigma, gall rust caused by the fungus Uromycladium falcatarium, the stem borer Xystrocera festiva, and mistletoe Scurrula sp. However, stem borer and gall rust were the only pest and disease issues recorded in the monocultures of Sengon in Indonesia. The occurrence of stem borer and gall rust disease had a significant effect on the diameter growth of trees and in some instances, these caused mortality of one-year-old trees. Significant mortality of four-year-old trees was caused by mistletoe infestation only. Although the incidence of gall rust and stem borer in the agroforestry system was not significantly low compared to the monoculture, the former had wider spacing between trees, more open canopy and resultant low humidity and faster wind speed reduced the severity of the gall rust disease and stem borer attack. However, the intercropping resulted in the white grub attack on young Sengon trees which calls for application of contaminant-free fertilizers in pineapple plantings.

Several forestry procedures affect tree volume and shape, such as spacing, pruning, and thinning. Studying and understanding the effect of these operations on stand attributes are very important for forest management. This study aimed to evaluate volume, form factor, and taper for Pinus taeda trees stratified into diameter classes within two planting spacings. In addition, we aimed to evaluate the time spent to scale each tree, measured with a chronometer. Indirect scaling was performed using a Criterion RD 1000. Thirty trees were scaled on each planting spacing (3 m x 2 m and 4 m x 2 m), totaling 60 trees encompassing all diameter classes. Tree volume was calculated using the Smalian equation. Tree volume, form factor, and taper were calculated to each tree and evaluated by stand (independent t-test) and diameter class (variance analysis and Tukey test). The average scaling time was 4 minutes and 35 seconds, which decreased with practice (-24%). Form factor and taper differed with spacing and diameter class. Volume did not differ with spacing, but it did in the diameter classes. We concluded that indirect scaling is a practical method for tree volume assessment; higher planting density leads to more cylindrical stems with lower taper ratios in comparison with denser stands; and the fact that tree volume, form factor and taper differed among the diameter classes should be incorporated into studies of taper modeling.

Abstract: In this study, we assessed the performance of different types of taper equations for predicting tree diameters at specific heights and total stem volumes for mixed stands of Taurus cedar ( Cedrus libani A. Rich.) and Taurus fir ( Abies cilicica Carr.). We used data from mixed stands containing a total of 131 cedar and 124 Taurus fir trees. We evaluated six commonly used and well-known forestry taper functions developed by a variety of researchers (Biging (1984), Zakrzewski (1999), Muhairwe (1999), Fang et al. (2000), Kozak (2004), and Sharma and Zhang (2004)). To address problems related to autocorrelation and multicollinearity in the hierarchical data associated with the construction of taper models, we used appropriate statistical procedures for the model fitting. We compared model performances based on the analysis of three goodness-of-fit statistics and found the compatible segmented model of Fang et al. (2000) to be superior in describing the stem profile and stem volume of both tree species in mixed stands. The equation used by Zakrzewski (1999) exhibited the poorest fitting results of the three taper equations. In general, we found segmented taper equations to provide more accurate predictions than variable-form models for both tree species. Results from the non-linear extra sum of squares method indicate that stem tapers differ among tree species in mixed stands. Therefore, a different taper function should be used for each tree species in mixed stands in the Bucak district. Using individual-specific taper equations yields more robust estimations and, therefore, will enhance the prediction accuracy of diameters at different heights and volumes in mixed stands. Keywords: Segmented model, compatible equation, stem form, merchantable volume, autocorrelation, F- test Received (Gelis): 08.02.2017 - Revised (Duzeltme): 17.03.2017 - Accepted (Kabul): 28.04.2017 Cite (Atif): Ozcelik, R., Dirican, O., 2017. Individual taper models for natural cedar and Taurus fir mixed stands of Bucak Region, Turkey. Journal of the Faculty of Forestry Istanbul University 67(2): 336-354. DOI: 10.17099/jffiu.290845