Stem volume functions for Melaleuca cajuputi trees in Southwestern Region

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.

Forest inventories are important tools for the management of forests. In this context, the estimation of the tree stem volume is a key issue. In this paper, we present a system for the estimation of forest stem diameter and volume at individual tree level from multireturn light detection and ranging (LIDAR) data. The proposed system is made up of a preprocessing module, a LIDAR segmentation algorithm (aimed at retrieving tree crowns), a variable extraction and selection procedure, and an estimation module based on support vector regression (SVR) (which is compared with a multiple linear regression technique). The variables derived from LIDAR data are computed from both the intensity and elevation channels of all available returns. Three different methods of variable selection are analyzed, and the sets of variables selected are used in the estimation phase. The stem volume is estimated with two methods: 1) direct estimation from the LIDAR variables and 2) combination of diameters and heights estimated from LIDAR variables with the species information derived from a classification map according to standard height/diameter relationships. Experimental results show that the system proposed is effective and provides high accuracies in both the stem volume and diameter estimations. Moreover, this paper provides useful indications on the effectiveness of SVR with LIDAR in forestry problems.

Currently, little information is available to estimate individual tree attributes for longleaf pine (Pinus palustris Mill.), an important tree species of the southeastern United States. The majority of available models are local, relying on stem diameter outside bark at breast height (dbh, cm) and not including stand-level parameters. We developed a set of individual tree equations to predict tree height (H, m), stem diameter inside bark at 1.37 m height (dbhIB, cm), stem volume outside bark (VOB, m 3 ), and stem volume inside bark (VIB ,m 3 ), as well as functions to determine merchantable stem volume ratio (both outside and inside bark) from the stump to any top diameter. Local and general models are presented for each tree attribute. General models included stand-level parameters such as age, site index, dominant height, basal area, and tree density. The user should decide which model type to use, depending on data availability and level of accuracy desired. To our knowledge, this is the first comprehensive individual tree-level set of equations reported for longleaf pine trees, including local and general models, which can be applied to longleaf pine trees over a large geographical area and across a wide range of ages and stand characteristics. The system presented here provides important new tools for supporting future longleaf pine management decisions.

Silvicultural treatment effects on commercial timber volume and functional composition of a selectively logged Australian tropical forest over 48 years

Estimating tree volume and biomass constitutes an essential part of the forest resources assessment and the evaluation of the climate change mitigation potential of forests through biomass accumulation and carbon sequestration. This research article provides stem volume and biomass equations applicable to five tree species, namely Afzelia africana Sm. (Caesalpiniaceae), Anogeissus leiocarpa (DC.) Guill. and Perr. (Combretaceae), Ceiba pentandra (L.) Gaertn. (Bombacaceae), Dialium guineense Willd. (Caesalpiniaceae), Diospyros mespiliformis Hochst. ex A.DC. (Ebenaceae) in natural protected tropical forests and, in addition, Tectona grandis L.f. (Verbenaceae) in plantations. In addition to the tree species specific equations, basic wood density, as well as carbon, nitrogen, organic matter and ash content were determined for these tree species in tropical conditions in West Africa. One hundred and sixty-two sample trees were measured through non-destructive sampling and analysed for volume and biomass. Stem biomass and stem volume were modelled as a function of diameter (at breast height; Dbh) and stem height (height to the crown base). Logarithmic models are presented that utilise Dbh and height data to predict tree component biomass and stem volumes. Alternative models are given that afford prediction based on Dbh data alone, assuming height data to be unavailable. Models that include height are preferred, having better predictive capabilities. Ranges in carbon, nitrogen and ash contents are given as well. The successful development of predictive models through the use of non-destructive methods in this study provide valuable data and tools for use in determining the contribution of these major African rainforest tree species to global carbon stocks, while ensuring the preservation of this valued African resource. This study needs to be expanded to further regions and tree species to complete a full inventory of all tree species, emphasising the relevance of African trees to carbon stocks at a global scale.

The objective of this paper was to investigate the impact of initial spacing and pre-commercial thinning (PCT) on tree growth, characteristics and stem quality in plantation-grown jack pine (Pinus banksiana Lamb.) after 58 years of growth. Four spacings including three initial spacings without PCT treatment, i.e., 1.52 × 1.52 m (5 × 5 ft), 2.13 × 2.13 m (7 × 7 ft) and 2.74 × 2.74 m (9 × 9 ft) and one initial spacing with PCT treatment (5 × 5 ft thinned to 7 × 7 ft at age 14), were chosen to analyze diameter at breast height (DBH) distribution, survival, and various tree and stem quality characteristics (e.g., DBH, total tree height, stem volume, crown size, branch, taper, sweep and wobbling). Tree mortality during the first 25 growth years was quite low for all four spacings, while after 25 years, survival for the four spacings rapidly declined. The decrease in survival for spacing 5 × 5 was the steepest, followed by spacings 7 × 7, 9 × 9 and finally the PCT-treated stand. DBH distributions for all four spacings were significantly different from each other, and five years after PCT, the 5 × 5 to 7 × 7 spacings had a similar DBH distribution to that of the constant 7 × 7 spacing. Mean DBHs differed significantly among the initial spacings. The 5 × 5 spacing produced significantly smaller trees than did the other three spacings through the years, and the 9 × 9 spacing produced significantly larger trees. PCT had positive effects on DBH growth, and yielded longer merchantable stems and better stem quality. PCT had little effect on crown development. Initial spacing significantly affected diameter growth, crown width and branch development, commercial stem length and volume, stem taper and stem deformation. Narrower spacing produced smaller but better quality stems. Spacing 7 × 7 had the worst stem quality in terms of overall sweep and wave-like transversal deformation (wobbling). A narrow initial spacing followed by a PCT treatment may provide a compromise solution for both tree growth and stem quality. Key words: Initial spacing, thinning, survival, tree growth, stem quality

Розглянуто проблеми, які виникли внаслідок набуття чинності нових стандартів на продукцію лісозаготівель. Невідповідність нормативно-інформаційної бази для таксації лісосік новим вимогам призводить до значних недоліків у плануванні виробничої діяльності лісогосподарських підприємств. Дослідження виконано на підставі дослідного матеріалу, зібраного в дубових насадженнях Придніпровського Правобережного Лісостепу на тимчасових пробних площах. Проаналізовано розподіл об'єму ділових стовбурів дуба звичайного (Quercus robur L.) на якісні категорії деревини залежно від діаметра, висоти та об'єму. Найбільш тісну лінійну залежність виявлено для абсолютних значень якісних категорій деревини від об'єму стовбура в корі. Між іншими біометричними показниками стовбура лінійна залежність відсутня або менш значуща на 5 %-му рівні. Завдяки аналізу модельовано вихід якісних категорій деревини залежно від об'єму стовбура на підставі степеневого рівняння. Пошук параметрів рівнянь виконано у MS Excel. Систематична похибка математичних моделей виходу ділової деревини виявилася близькою до нуля (1,0 %), дров та відходів – у допустимих межах (5,1 та 8,0 %), що дало змогу прийняти їх для розробки відповідних таблиць. Опрацьовані таблиці дають змогу за новими стандартами прогнозувати розподіл об'єму ділових стовбурів дуба зі стандартною похибкою 0,063-0,118 м3. Для отримання даних розподілу об'єму ділової деревини за класами розмірів, передбачених ДСТУ 1315-1-2011, розроблено в системі R алгоритм умовного розкряжування модельних дерев. Він оснований на апроксимації твірної поверхні стовбура за допомогою математичної моделі твірної A. Kozak (1988). На підставі одержаного розподілу об'єму ділової деревини за класами діаметрів досліджено його залежність від біометричних показників стовбурів. Практично для всіх розмірних категорій деревини виявлено нелінійний зв'язок. Узагальнення розмірної структури ділової деревини проведено за методикою, яка базується на дослідженні закономірностей розподілу об'єму за класами розмірів у відносних величинах. Виявлено тісну залежність відносних величин розмірної структури від діаметра модельних дерев на висоті 1,3 м. Незначна систематична похибка отриманих математичних моделей розподілу ділової деревини (-1,1-0,9 %) дала змогу прийняти їх для складання об'ємних таблиць. Розроблені за новими стандартами таблиці забезпечують прогнозування розподілу об'єму ділової деревини ділових стовбурів дуба за класами розмірів залежно від серединного діаметра лісоматеріалів без кори.

Sustainable forest management requires accurate estimates of wood volume. At present, red pine (Pinus resinosa Sol. ex Aiton) is the most widely planted conifer tree species in southern Ontario, Canada. Therefore, inside and outside bark volume equations were developed for red pine trees grown in plantations. One hundred and fifty red pine trees were sampled from 30 even-aged plantations from across Ontario, Canada. Height-diameter pairs along the boles of sampled trees used to calculate stem volumes were obtained from stem analysis. Equations fitted to the data were a combined variable, modified combined variable, and modified form of dimensionally compatible volume equations. These equations were compared for their goodness-of-fit statistics, logical consistency, and predictive accuracy. The goodness-of-fit characteristics for all three equations were comparable for both inside and outside bark volumes. However, the estimated values for the intercept for the modified form of the dimensionally compatible and modified combined variable volume equations were negative and nonsignificant. The combined variable volume equation resulted in logically consistent parameter estimates in the presence of random effects parameters. Therefore, this equation was selected as the inside and outside bark volume equation for red pine trees grown in plantations. A nonlinear mixed-effects modeling approach was applied in fitting the final volume equation that included a weight (power function) to address heteroscedasticity. The equations developed here can be used to calculate inside and outside bark volumes of red pine plantations in boreal forests in Eastern Canada. These equations would require both diameter at breast height (DBH) and total height values in meters.

Modelling stem taper and volume is crucial in many forest management and planning systems. Taper models are used for diameter prediction at any location along the stem of a sample tree. Furthermore, taper models are flexible means to provide information on the stem volume and assortment structure of a forest stand or other management units. Usually, taper functions are mean functions of multiple linear or nonlinear regression models with diameter at breast height and tree height as predictor variables. In large-scale inventories, an upper diameter is often considered as an additional predictor variable to improve the reliability of taper and volume predictions. Most studies on stem taper focus on accurately modelling the mean function; the error structure of the regression model is neglected or treated as secondary. We present a semi-parametric linear mixed model where the population mean diameter at an arbitrary stem location is a smooth function of relative height. Observed tree-individual diameter deviations from the population mean are assumed to be realizations of a smooth Gaussian process with the covariance depending on the sampled diameter locations. In addition to the smooth random deviation from the population average, we consider independent zero mean residual errors in order to describe the deviations of the observed diameter measurements from the tree-individual smooth stem taper. The smooth model components are approximated by cubic spline functions with a B-spline basis and a small number of knots. The B-spline coefficients of the population mean function are treated as fixed effects, whereas coefficients of the smooth tree-individual deviation are modelled as random effects with zero mean and a symmetric positive definite covariance matrix. The taper of a tree is predicted using an arbitrary number of diameter and corresponding height measurements at arbitrary positions along the stem to calibrate the tree-individual random deviation from the population mean estimated by the fixed effects. This allows a flexible application of the method in practice. Volume predictions are calculated as the integral over cross-sectional areas estimated from the calibrated taper curve. Approximate estimators for the mean squared errors of volume estimates are provided. If the tree height is estimated or measured with error, we use the “law of total expectation and variance” to derive approximate diameter and volume predictions with associated confidence and prediction intervals. All methods presented in this study are implemented in the R-package TapeR.

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.

Airborne polarimetric Synthetic Aperture Radar (SAR) is used for estimating the stem volume of a Finnish boreal forest by comparing different empirical models. Its capability for retrieval of snow water equivalent is then explored. Fully polarimetric L-and C-band data were acquired over a Finnish test site in March and May 1995. The information content was explored qualitatively by inspecting polarimetric colour composites, and by applying decomposition algorithms to the polarimetric covariance matrices at individual frequencies. Three families of quantitative models were fitted to estimate stem volume: (1) F1P1 models, using a single frequency and a single polarization; (2) F2P1 models, using the difference between HV polarization at C- and L-band related to stem volume; (3) F1P4 models, based on a single frequency and the full polarimetric information, selected by stepwise multiple regression with stem volume. Stem volume estimates from SAR are compared with digital stem volume data by the Finnish Forest Research Institute. Prior information about the stem volume distribution addresses the saturation problem of the microwave response. The L-band F1P4 models in March and May 1995 have the smallest rms errors, around 22 m 3 ha - 1 . Three multiple regression models to retrieve snow water equivalent from backscatter are presented: (1) EU model, an explorative, uncorrected multiple regression model; (2) EC model, an explorative, stem volume corrected multiple regression model; (3) CC model, a statistically conservative, stem volume corrected multiple regression model. The accuracy of snow water equivalent estimates was improved significantly by a simple linear correction for stem volume. The statistically conservative CC model showed that only L-band in HH polarization explained a significant ( p <0.05) proportion of snow water equivalent ( r 2 =0.51). The explorative EC model resulted in r 2 =0.68 ( p >0.05). Conclusions are that (1) decomposition algorithms of the polarimetric covariance matrix result in information on scattering mechanisms in the vegetation canopy and on the ground, so being potentially of great value for land cover mapping; (2) satellite polarimetric SARs, for example those to be flown on Envisat and ALOS, will be able to estimate stem volume on continental and global scales; and (3) L-band SAR has a potential for snow cover mapping and runoff prediction.

The study was performed to find the growth pattern by stem analysis of Korean white pine (Pinus koraiensis) in the Central Northern Region of Korea. One standard tree from each of 16 sites was stemmed and analyzed for the study. For sampled trees, the age range was 16–77 years, diameter at breast height (DBH) was 15.8–44.4 cm, height was 9.3–24.0 m, and stem volume was 0.1002–1.8518 m3. The stem volumes by our study had higher values over 40 DBH compared to Korea Forest Research Institute measurements. The bark volume had no particular trend with DBH and height, while bark ratio tended to decrease with DBH and height. The DBH and height curves by age had a concave shape whereas volume curve had a convex shape. The average periodic annual increment (PAI) of DBH was the highest at age 15 (1.0 cm/yr), and the highest value of the mean annual increment (MAI) of DBH was 0.7 cm/yr at age 30. The highest values of PAI and MAI of height were 0.6 m/yr (age 15) and 0.5 m/year (age 25) respectively. The average PAI and MAI of volume continued to increase even after age 75. Growth percentages of DBH, height and volume tended to decrease with age, particularly rapidly at age 20–30. Volume growth percentage was much higher than diameter and height.

Poplar hybrids were grown with irrigation in a large-scale plantation to investigate the mechanisms underlying clonal differences in drought resistance. Beginning in spring 1992, Populus trichocarpa x P. deltoides (TD) and P. deltoides x P. nigra (DN) cuttings received 46, 76, or 137 cm year(-1) of irrigation to supplement the 18-20 cm of annual precipitation, and all trees received the same fertilization regime. Stem volume, assessed as the square of stem diameter at breast height times tree height (D(2)H), and water relations of the trees were studied from the end of their second growing season until the end of their fifth growing season. By the end of the second growing season, stem volume of Clone TD was 40-146% larger than that of Clone DN, but stem volume growth was independent of irrigation in excess of 46 cm year(-1) in both clones. During the third growing season, stem volume growth of both clones was limited by both the 46- and 76-cm irrigation treatments, so that by the end of the third growing season trees in the 46-cm irrigation treatment were only half the size of trees in the 137-cm irrigation treatment. These treatment differences were maintained through the fifth growing season. Although stem volumes of Clone TD trees in the 76- and 137-cm irrigation treatments were larger than the corresponding values for Clone DN trees at the end of the third growing season (1994), these clonal differences gradually decreased in subsequent years and were not detectable after 5 years, because stem volume relative growth rate of Clone DN was greater than that of Clone TD in all treatments. Although both clones exhibited similar predawn leaf water potentials, Clone DN typically maintained higher midday leaf water potentials, suggesting better stomatal control of water loss. Clonal and treatment differences in osmotic potential at full turgor were minimal and could not explain the clonal differences in drought resistance. Root density and root density to stem volume ratio increased more in response to moderate drought in Clone DN than in Clone TD, resulting in enhanced drought resistance (high stem volume growth rate under moderate drought conditions) and an increased capacity to withdraw water from the soil. We conclude that the greater drought resistance of Clone DN compared with Clone TD was the result of the maintenance of a more favorable water balance by stomatal regulation and greater carbon allocation to roots during the early stages of drought. However, the low root density to stem volume ratio in Clone DN growing in the 46-cm irrigation treatment suggests that severe water limitation restricted the preferential allocation of carbon to belowground tissues, so that both root and shoot growth were constrained by severe drought.

Accurate estimates of tree bole volume are fundamental to sustainable forest management. Total inside and outside bark and merchantable volume equations were developed for 25 major commercial tree species grown in natural stands in eastern and central Canada and the northeastern United States. Data used to develop these equations was collected from 9647 trees sampled from natural stands across the study area. The number of trees sampled varied among species. Jack pine (Pinus banksiana Lamb.) had the most observations (1648 trees) and American basswood (Tilia americana) and red oak (Quercus rubra L.) had the fewest (28 trees each). Two mathematically consistent volume equations (dimensionally compatible and combined variable) were fitted to inside and outside bark and merchantable tree volume data from these tree species. The final volume equation was selected based on fit statistics, predictive accuracy, and logical consistency. Its predictive accuracy was compared with a volume equation previously developed by Honer. Both (total and merchantable) volume equations were fitted using a nonlinear mixed-effects modelling approach. However, random effects were significant for total volumes for only four tree species. A weight (power function) was used to address heteroscedasticity in the data. The modified form of the dimensionally compatible volume equation outperformed the combined variable volume equation in terms of fit statistics and predictive accuracy and was selected as the total inside and outside bark and merchantable volume equations for all tree species. This equation produced logically consistent estimates of total and merchantable volumes and was more accurate than that previously developed by Honer to estimate volumes for most of the tree species used in this study. This new equation can be used to estimate total inside and outside bark and merchantable volumes of major commercial tree species in eastern and central Canada and the northeastern United States.

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