Stem Volume Estimation Research Articles

Mobile laser scanning as reference for estimation of stem attributes from airborne laser scanning

The acquisition of high-quality reference data is essential for effectively modelling forest attributes. Incorporating close-range Light Detection and Ranging (LiDAR) systems into the reference data collection stage of remote sensing-based forest inventories can not only increase data collection efficiency but also increase the number of attributes measured with high quality. Therefore, we propose a model-based forest inventory method that uses reference data collected by a car-mounted mobile laser scanning (MLS) system along boreal forest roads. This approach is used for the estimation of diameter at breast height (DBH) and stem volume at the individual tree-level from airborne laser scanning (ALS) data. In addition, we compare the estimates obtained using the proposed method with the ones derived from reference data collected by traditional field inventory of 265 field plots systematically distributed over the study area. The accuracy of the estimates remained comparable regardless of the reference dataset used for estimation of DBH and stem volume. When using the field inventory dataset for model training, the root mean square error (RMSE) of DBH estimates were 4.06 cm (18.8 %) for Norway spruce trees, 6.3 cm (29.6 %) for Scots pine and 8.61 cm (55.9 %) for deciduous trees. Similarly, when evaluating predictions based on the MLS dataset as reference, RMSEs were equal to 3.97 cm (18.4 %) for Norway spruce, 6.12 cm (28.8 %) for Scots pine, and 8.98 cm (58.3 %) for deciduous trees. In general, biases were below 1 cm for most species classes, with the exception of deciduous trees. The accuracy of stem volume also had RMSEs varying across different tree species. For the estimates based on traditional field inventory, the RMSEs were 0.176 m3 (38.8 %) for Norway spruce, 0.228 m3 (52.4 %) for Scots pine and 0.246 m3 (158 %) for deciduous trees. When using the MLS dataset as a reference, the RMSEs were equal to 0.176 m3 (38.8 %), 0.228 m3 (52.4 %), and 0.246 m3 (158 %) for Norway spruce, Scots pine, and deciduous trees, respectively. Car-mounted MLS demonstrated its potential as an efficient alternative for collecting reference data in remote sensing-based forest inventories, which could complement traditional methods.

Evaluating the transferability of airborne laser scanning derived stem size prediction models for Pinus taeda L. stem size estimation to two different locations and acquisition specifications

ABSTRACT Airborne laser scanning (ALS) datasets are used widely for estimating forest biometrics. The transferability of predictive models among ALS acquisitions is a topic of research due to differences in timing, flight parameters, equipment specifications, environmental conditions, and processing methods. The transferability of predictive models therefore is subject to uncertainty. This paper presents an evaluation of the transferability of models for the estimation of stem volume and diameter at breast height (DBH) based on individual tree crown size and competitive neighbourhood metrics derived for managed loblolly pine (Pinus taeda) and slash pine (Pinus elliottii) forest in the Southern USA. Two predictive models types were tested: multiple linear regression (MLR) and Rand Forest (RF). We also evaluated the inclusion of additional training data to model development. Models were able to be transferred to other locations with similar structural and management conditions as the original training dataset with little decrease in accuracy, specifically unthinned stands, despite different ALS acquisitions (Plot stem volume: R2 0.7–0.8; NRMSE 10–12%; mean DBH: R2 0.4–0.7; NRMSE 10–17%; plot basal area: R2 0.7–0.8; NRMSE 12%). Increases in structural differences between the training and test data, driven by age or thinning status, introduced unacceptable levels of uncertainty (Stem volume: R2 0.4–0.7; NRMSE 12–16%; mean DBH: R2 0.4–0.5; NRMSE 18–20%; plot basal area: R2 0.5–0.6; NRMSE 22–40%). Generally, RF models most accuracy estimated DBH, and MLR for stem volume. Improvements to estimate accuracy can be achieved through the addition of relatively small datasets, representing features which were not present in the original data. ALS’s ability to provide accurate and near-complete inventories of forests hold a great deal of potential for forest management. The existence of a transferable model that can be used across different acquisitions represents a saving in terms of cost and time, we would argue that future research is therefore warranted.

Integration of Terrestrial Laser Scanning and field measurements data for tree stem volume estimation: Exploring parametric and non-parametric modeling approaches

Integration of Terrestrial Laser Scanning and field measurements data for tree stem volume estimation: Exploring parametric and non-parametric modeling approaches

Feasibility of using Ku-band helicopter-borne microwave radar for stem volume and biomass estimation in boreal forest

Under the global climate challenges, accurate assessment of forest variables is becoming increasingly important for effective forest management and monitoring. While long-wavelength satellite radar data (P-, L-band) has been widely used for this purpose, the potential of airborne Ku-band microwave radar remains underexplored. In this paper, an airborne Ku-band frequency modulated continuous wave (FMCW) profiling radar data was used to predict forest variables including plot-level basal-area weighted mean canopy height (Hg), mean diameter at breast height (DBHg), stem volume (V) and above ground biomass (AGB) using the random forest method. In addition, the maximum canopy heights were computed from the radar-derived results. The estimated results were compared with 55 manually-measured and accurately matched field plots consisting of thousands of trees. The comparison results show that the estimation accuracy is at a good level, with the relative Root Mean Square Errors (RMSE%) and the coefficient of determination (R2) of the four variables were Hg (10.04 %, 0.75), DBHg (17.25 %, 0.63), V (21.11 %, 0.67) and AGB (19.75 %, 0.63), respectively. The estimation of plot-level maximum heights resulted in a relative RMSE of 7.95 % and R2 of 0.89. Through comparing with previous similar studies, the accuracies of estimating the four variables from airborne Ku-band data are comparable to those of high-precision satellite microwave radar data. The study results indicate that the canopy gaps and adequate penetration of airborne Ku-band signals into the canopy enable the characterization of the canopy layer and the ground floor, allowing for accurate estimation of forest variables in boreal forests.

Integrating personal laser scanning with uncrewed aerial vehicle-based photogrammetry or laser scanning for accurate stem volume estimation in temperate coniferous forests

ABSTRACT An extensive number of trees are surveyed for logging purposes, necessitating efficient and precise logging survey methods. Integrating over- and under-canopy remote sensing, such as personal laser scanning (PLS) with uncrewed aerial vehicle-based laser scanning (ULS) or digital aerial photogrammetry (DAP), is a promising method. In this study, we aimed to estimate stem volume in a 16.89-ha coniferous forest using these techniques at the individual, plot, and stand levels. The root mean square error (RMSE) and relative RMSE (rRMSE) when compared to conventional field surveys of PLS-based volume estimations were 0.14 m3 (21.6%) before and 0.08 m3 (12.3%) after bias correction. When integrating PLS with ULS and DAP, the RMSE and rRMSE values were 0.16 m3 (26.7%) and 0.16 m3 (27.0%), respectively. The F-score for the individual tree detection analysis by ULS and DAP were 0.94 and 0.96, respectively. The RMSE of the estimated volume in the plots was 0.08 m3 for both ULS and DAP. The estimated volumes of timber produced in the stand using the utilization rate overestimated the actual volume by 30.6%, 13.0%, and 17.0%, for PLS, ULS, and DAP, respectively. While the individual stem volume estimation accuracy of ULS and DAP was lower than that of the field survey, at the plot level the results were comparable, with ULS and DAP showing results significantly closer to the actual results than those of PLS at the stand level. This study highlights the potential for integrating PLS with uncrewed aerial vehicle methods for estimating stem and log volumes at the plot and stand levels.

Volume Estimation of Stem Segments Based on a Tetrahedron Model Using Terrestrial Laser Scanning Data

Stem volume is a very important parameter in forestry inventory and carbon storage. The stem volume estimated by most existing methods deviates from its true value because the irregularity of the stem is usually overlooked. In this study, we propose a stem segment volume estimation based on the tetrahedron model using TLS data. First, the initial stem segment surface model, including the lower, upper, and outer triangular surface models, was gradually reconstructed. Next, the outer surface model was subdivided based on the edge subdivision. Then, a closed triangular surface model without self-intersection was obtained. Afterward, a tetrahedron model of the stem segment was generated using TetGen software (Version 1.6.0) for the triangular surface model. Finally, the stem segment volume was calculated by summing the volumes of all the tetrahedrons in the tetrahedron model. An experiment with 76 stem segments from different tree species with different parameters showed that the reconstructed stem segment surface model effectively reflected the geometrical features of the stem segment surface. Compared to the volume based on the simulated sectional measurement, the MAPE of the volume based on the tetrahedron model was 2.12%. The results demonstrated the validity of the presented method for stem surface reconstruction and stem volume estimation, and the volume based on the tetrahedron model was closer to the true value than that based on the sectional measurement.

Taper, volume, and bark thickness models for spruce, pine, and birch in Norway

ABSTRACT Taper models, which describe the shape of tree stems, are central to estimating stem volume. Literature provides both taper- and volume models for the three main species in Norway, Norway spruce, Scots pine, and birch. These models, however, were mainly developed using approaches established over 50 years ago, and without consistency between taper and volume. We tested eleven equations for taper and six equations for bark thickness. The models were fitted and evaluated using a large dataset covering all forested regions in Norway. The selected models were converted into volume functions using numerical integration, providing both with- and without-bark volumes and compared to the volume functions in operational use. Taper models resulted in root mean squared error (RMSE) of 7.2, 7.9, and 9.0 mm for spruce, pine, and birch respectively. Bark thickness models resulted in RMSE of 2.5, 6.1, and 4.1 mm, for spruce, pine, and birch respectively. Validation of volume models with bark resulted in RMSE of 12.7%, 13.0%, and 19.7% for spruce, pine, and birch respectively. Additional variables, tree age, site index, elevation, and live crown proportion, were tested without resulting in any strong increase in predictive power.

Stem Profile Patterns ofPinus nigraandPinus sylvestrisGrowing in Mixed Stands

AbstractTaper equations provide one of the most successful approaches of calculating tree volume to specified top diameters from standing tree measurements. This study assessed the stem profile patterns of Black pine (Pinus nigra Arnold.) and Scots pine (Pinus sylvestris L.) trees growing in mixed stands in northwestern Türkiye using a segmented polynomial taper equation. Models were fitted with the continuous second-order autoregressive structure to correct for the autocorrelation. The models fit the data well, describing more than 99%, 98%, and 97% of variation in diameter, merchantable volume, and total stem volume, respectively. However, the prediction errors were slightly larger for black pine than for Scots pine. Results also revealed that the model coefficients for these species were significantly different. Models developed in this study should provide more accurate upper stem diameter and volume estimates when the objective is to estimate such attributes for black pine and Scots pine growing in the mixed stands.Study Implications: Estimates of total and merchantable tree volume in a stand are essential for forest management and planning. Taper models are one of the most accurate approaches to estimating upper stem diameters and volume to any merchantability limit. There has been an increasing interest in managing mixed-species stands but limited work has been done on taper equations for trees growing in mixed stands. This study assessed the stem profile patterns of black pine and Scots pine trees growing in mixed-species stands in northwestern Türkiye. As has been reported for pure stands, species-specific taper equations were more accurate upper stem diameter and volume estimations in mixed-species stands. The developed taper models should play an important role in planning and inventorying mixed Black pine and Scots pine stands in Türkiye.

Using terrestrial laser scanning to evaluate non-destructive aboveground biomass allometries in diverse Northern California forests

A crucial part of carbon accounting is quantifying a tree’s aboveground biomass (AGB) using allometric equations, but species-specific equations are limited because data to inform these equations requires destructive harvesting of many trees which is difficult and time-consuming. Here, we used terrestrial laser scanning (TLS) to non-destructively estimate AGB for 282 trees from 5 species at 3 locations in Northern California using stem and branch volume estimates from quantitative structure models (QSMs) and wood density from the literature. We then compared TLS QSM estimates of AGB with published allometric equations and used TLS-based AGB, diameter at breast height (DBH), and height to derive new species-specific allometric AGB equations for our study species. To validate the use of TLS, we used traditional forestry approaches to collect DBH (n = 550) and height (n = 291) data on individual trees. TLS-based DBH and height were not significantly different from field inventory data (R2 = 0.98 for DBH, R2 = 0.95 for height). Across all species, AGB calculated from TLS QSM volumes were approximately 30% greater than AGB estimates using published Forest Service’s Forest Inventory and Analysis Program equations, and TLS QSM AGB estimates were 10% greater than AGB calculated with existing equations, although this variation was species-dependent. In particular, TLS AGB estimates for Quercus agrifolia and Sequoia sempervirens differed the most from AGB estimates calculated using published equations. New allometric equations created using TLS data with DBH and height performed better than equations that only included DBH and matched most closely with AGB estimates generated from QSMs. Our results support the use of TLS as a method to rapidly estimate height, DBH, and AGB of multiple trees at a plot-level when species are identified and wood density is known. In addition, the creation of new TLS-based non-destructive allometric equations for our 5 study species may have important applications and implications for carbon quantification over larger spatial scales, especially since our equations estimated greater AGB than previous approaches.

The use of dual-wavelength airborne laser scanning for estimating tree species composition and species-specific stem volumes in a boreal forest

The estimation of species composition and species-specific stem volumes are critical components of many forest inventories. The use of airborne laser scanning with multiple spectral channels may prove instrumental for the cost-efficient retrieval of these forest variables. In this study, we scanned a boreal forest using two channels: 532 nm (green) and 1064 nm (near infrared). The data was used in a two-step methodology to (1) classify species, and (2) estimate species-specific stem volume at the level of individual tree crowns. The classification of pines, spruces and broadleaves involved linear discriminant analysis (LDA) and resulted in an overall accuracy of 91.1 % at the level of individual trees. For the estimation of stem volume, we employed species-specific k-nearest neighbors models and evaluated the performance at the plot level for 256 field plots located in central Sweden. This resulted in root-mean-square errors (RMSE) of 36 m3/ha (16 %) for total volume, 40 m3/ha (27 %) for pine volume, 32 m3/ha (48 %) for spruce volume, and 13 m3/ha (87 %) for broadleaf volume. We also simulated the use of a monospectral near infrared (NIR) scanner by excluding features based on the green channel. This resulted in lower overall accuracy for the species classification (86.8 %) and an RMSE of 41 m3/ha (18 %) for the estimation of total stem volume. The largest difference when only the NIR channel was used was the difficulty to accurately identify broadleaves and estimate broadleaf stem volume. When excluding the green channel, RMSE for broadleaved volume increased from 13 to 26 m3/ha. The study thus demonstrates the added benefit of the green channel for the estimation of both species composition and species-specific stem volumes. In addition, we investigated how tree height influences the results where shorter trees were found to be more difficult to classify correctly.

Regional Stem Volume Mapping: A Feasibility Assessment of Scaling Tree-Level Estimates

Spatially detailed monitoring of forest resources is important for sustainable management but limited by a lack of field measurements. The increasing availability of multisource datasets offers the potential to characterize forest attributes at finer resolutions with regional coverage. This study aimed to assess the potential of mapping stem volume at a 30 m scale in eastern Texas using multisource datasets: airborne lidar, Landsat and LANDFIRE (Landscape Fire and Resource Management Planning Tools Project) datasets. Gradient-boosted trees regression models relating total volume, estimated from airborne lidar measurements and allometric equations, and multitemporal Landsat and LANDFIRE predictors were developed and evaluated. The fitted models showed moderate to high correlation (R2 = 0.52–0.81) with reference stem volume estimates, with higher correlation in pine forests (R2 = 0.70–0.81) than mixed forests (R2 = 0.52–0.67). The models were also precise, with relative percent mean absolute errors (pMAE) of 13.8–21.2%. The estimated volumes also consistently agreed with volumes estimated in independent sites (R2 = 0.51, pMAE = 34.7%) and with US Forest Service Forest Inventory Analysis county-level volume estimates (R2 = 0.93, pBias = −10.3%, pMAE = 11.7%). This study shows the potential of developing regional stem volume products using airborne lidar and multisource datasets, supporting forest productivity and carbon modeling at spatially detailed scales.

Modeling compatible taper and stem volume of pure Scots pine stands in Northeastern Turkey

Compatible taper and volume equations for pure and natural Scots pine stands in the northeastern part of Turkey (Ardahan Province) were developed using a nonlinear mixed-effects modeling approach. Experimental data were obtained from 137 felled sample trees in different diameter and height classes. The most successful model (Jiang et al. 2005) explained 98.3% of the variance in stem diameter estimation and the RMSE, ME, MAE, AIC and BIC value obtained using this model were 1.955 cm, 0.043 cm, 1.300 cm, 9783.8 and 9812.6, respectively. Considering the criterion values of AIC, BIC and -2LnL, the model with random-effects in two parameters (b1 and b3) was the most successful for Scots pine. While the mixed model including random parameters did not completely solved the problem of the autocorrelation of errors in this study, the use of the autoregressive error structure AR(1) eliminated the autocorrelation in the residuals. In addition, the best estimation results among 20 different calibration options were obtained using the option of measuring two tree diameters at d1.30 and d5.30 with validation data. The most successful model explained 99.18% of the total variance in stem volume estimation in Scots pine.

Estimation of individual stem volume and diameter from segmented UAV laser scanning datasets in Pinus taeda L. plantations

ABSTRACT The competitive neighbourhood surrounding an individual tree can have a significant influence on its diameter at breast height (DBH) and individual tree stem volume (SV). Distance dependent competition index metrics are rarely recorded in traditional field campaigns because they are laborious to collect and are spatially limited. Remote sensing data could overcome these limitations while providing estimation of forest attributes over a large area. We used unoccupied aerial vehicle laser scanning data to delineate individual tree crowns (ITCs) and calculated crown size and distance-dependent competition indices to estimate DBH and SV. We contrasted two methods: (i) Random Forest (RF) and (ii) backwards-stepwise, linear multiple regression (LMR). We utilized an existing experiment in Pinus taeda L. plantations including multiple planting densities, genotypes and silvicultural levels. While the tree planting density did affect the correct delineation of ITCs, between 61% and 99% (mean 86%) were correctly linked to the planting location. The most accurate RF and LMR models all included metrics related to ITC size and competitive neighbourhood. The DBH estimates from RF and LMR were similar: RMSE 3.05 and 3.13 cm (R2 0.64 and 0.62), respectively. Estimates of SV from RF were slightly better than for LMR: RMSE 0.06 and 0.07 m3 (R2 0.77 and 0.70), respectively. Our results provide evidence that ITC size and competition index metrics may improve DBH and SV estimation accuracy when analysing laser-scanning data. The ability to provide accurate, and near-complete, forest inventories holds a great deal of potential for forest management planning.

Upper stem diameter and volume prediction strategies in the National Forest Inventory of Finland

In forest inventories, field data are needed for the prediction of tree volumes. However, gathering field data requires resources, such as labour, equipment, and data management operations. This means that time and budget, as well as quality, must be carefully considered when National Forest Inventory (NFI) field measurement activities are planned. Therefore, the development of cost efficient, simple, safe and reliable measurement methods and tools are of great interest. To date, upper stem diameter (d6), which provides a more reliable estimation of tree stem volume, has typically been measured with a parabolic calliper. In this study, the performance of the Criterion laser-based dendrometer was examined for d6 measurements. A total of 326 sample trees were measured multiple times with three different measurement instruments. These instruments were used to measure diameter at breast height (dbh) as well as d6 measurements. Bland-Altman plots and measurement error variances were used to determine measurement instrument reliability. For all trees, the standard deviation for the laser based dendrometer was 18.73 mm at dbh and 15.36 mm for the d6 measurements. When the performance of Criterion was analysed with reference to the mean value of repeated measurements, the standard deviation in the dbh measurements was 12.21 mm, and 8.88 mm in the d6 measurements.

Diameter and stem volume estimation based on under canopy UAV-SfM-MVS survey approach in subtropical forest of Okinawa Island, Japan

Diameter and stem volume estimation based on under canopy UAV-SfM-MVS survey approach in subtropical forest of Okinawa Island, Japan

Height-diameter relationships and stem volume equations in young and middle-aged forest stands of Ukraine

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

Tree stem volume estimation from terrestrial LiDAR point cloud by unwrapping

Estimating the volume of standing trees is a fundamental concern in forestry and is typically accomplished using one or more measurements of stem diameter along with formulae that assume geometric primitives. In contrast, technologies such as terrestrial Light Detection And Ranging (LiDAR) can record very detailed spatial information on the actual surface of an object, such as a tree bole. We present a method using LiDAR that provides accurate volume estimates of tree stems, as well as 2D rasters that display details of stem surfaces, which we call the “unwrapping method.” This method combines the concepts of cylinder fitting, voxelization, and digital elevation models. The method is illustrated and tested using a sample of standing trees, whereby we are able to generate accurate volume estimates from the point cloud, as well as accurate visualization of the scanned stem sections. When compared to volume estimates derived from Huber's, Smalian's, and Newton's formulae, the differences are consistent with previous studies comparing formula-derived volume estimates and water-displacement-derived volume estimates, suggesting the unwrapping method has comparable accuracy to water displacement.

Compatible Stem Volume and Stem Diameter Equations for Brutian Pine Stands in Antalya-Gebiz Region

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.

Stem volume by height classes of immature, mature and overmature stands of the main forest-forming species of Ukraine

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

Development of a Climate-Sensitive Structural Stand Density Management Model for Red Pine

The primary objective of this study was to develop a climate-sensitive modular-based structural stand density management model (SSDMM) for red pine (Pinus resinosa Aiton) plantations situated within the western Great Lakes—St. Lawrence and south-central Boreal Forest Regions of Canada. For a given climate change scenario (e.g., representative concentration pathway (RCP)), geographic location (longitude and latitude), site quality (site index) and crop plan (e.g., initial espacement density and subsequent thinning treatments), the resultant hierarchical-based SSDMM consisting of six integrated modules, enabled the prediction of a multitude of management-relevant performance metrics over rotational lengths out to the year 2100. These metrics included productivity measures (e.g., mean annual volume, biomass and carbon increments), volumetric yield estimates (e.g., total and merchantable volumes), pole and log product distributions (e.g., number and size distribution of pulp and saw logs, and utility poles), biomass production and carbon sequestration outcomes (e.g., oven-dried masses of above-ground components and associated carbon mass equivalents), recoverable end-product volumes and associated monetary values (e.g., volumes and economic worth estimates of recovered chip and dimensional lumber products extractable via stud and randomized length mill processing protocols), and crop tree fibre attributes reflective of end-product potential (e.g., wood density, microfibril angle, and modulus of elasticity). The core modules responsible for quantifying stand dynamics and structural change were developed using 491 tree-list measurements and 146 stand-level summaries obtained from 98 remeasured permanent sample plots situated within 21 geographically separated plantation-based initial spacing and thinning experiments distributed throughout southern and north-central Ontario. Computationally, the red pine SSDMM and associated algorithmic analogue (1) produced mathematically compatible stem and end-product volume estimates, (2) accounted for density-dependent as well as density-independent mortality losses, response delay following thinning and genetic worth effects, (3) enabled end-users to specify merchantability standards (log and pole dimensions), product degrade factors and cost profiles, and (4) addressed climate change impacts on rotational yield outcomes by geo-referencing RCP-specific effects on stand dynamical processes via the deployment of a climate-driven biophysical site-based height-age model. In summary, the provision of the red pine SSDMM and its unique ability to account for locale-specific climate change effects on crop planning forecasts inclusive of utility pole production, should be of consequential utility as the complexities of silvicultural decision-making intensify during the Anthropocene.