Equations for predicting tree height, total volume, and product recovery for black spruce (Picea mariana) plantations in northeastern  Quebec

Several regression models with different independent variables were studied for their ability to predict total tree height, total stem volume, and product recoveries (lumber volume, chip volume, lumber value, and total product value) from a sawing simulator. A sample of 172 trees from black spruce plantations was used to fit model parameters and another independent sample of 139 trees was used for model evaluation. The sample encompassed large variations in tree characteristics and tree product recovery. All the fitted models were suitable for predicting their corresponding response variables. Model validation through actual product recovery data from a real stud mill further indicated that the general tree-level models for the product recovery were able to accurately predict product recovery, especially from small- and medium-sized trees, using measured tree characteristics. These models provide a valuable tool for forest managers in determining appropriate management strategies (e.g., stand volume and optimizing stand value). Key words: black spruce, regression analysis, tree characteristics, product recovery, sawing simulation

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Models for predicting product recovery using selected tree characteristics of black spruce

Canadian Journal of Forest Research ◽

10.1139/x05-025 ◽

2005 ◽

Vol 35 (4) ◽

pp. 930-937 ◽

Cited By ~ 23

Author(s):

Chuangmin Liu ◽

S Y Zhang

Keyword(s):

Regression Models ◽

Black Spruce ◽

Tree Height ◽

Product Recovery ◽

Second Order ◽

Statistical Regression ◽

Ann Model ◽

Back Propagation Algorithm ◽

Order Polynomial ◽

Tree Characteristics

The artificial neural network (ANN) model and five traditional statistical regression models were used to predict four parameters of simulated product recovery (lumber volume, lumber value, chip volume, and total product value) from the stud mill simulation based on three basic tree characteristics of black spruce (i.e., diameter at breast height (DBH), tree height, and tree taper). The ANN model (i.e., the three-layer perceptron with error back-propagation algorithm) performed as well as or better than the five statistical regression models in terms of statistical criteria such as R2, root mean square error, and mean absolute error of predictions. The second-order polynomial with both DBH and tree height predicted the four product recoveries as accurately as the ANN model. This study showed that the ANN model, the second-order polynomial function, and the power function were suitable for the prediction of product recovery using the selected tree characteristics. The models developed in this study allow the estimation of the product recovery of individual trees and of a forest stand before it is harvested. It is evident that these models would be valuable tools for forest resource managers.

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Modelling the relationship of tree-level product value with tree characteristics in black spruce

The Forestry Chronicle ◽

10.5558/tfc82690-5 ◽

2006 ◽

Vol 82 (5) ◽

pp. 690-699 ◽

Cited By ~ 4

Author(s):

S Y Zhang ◽

Y C Lei ◽

Z H Jiang

Keyword(s):

Black Spruce ◽

Tree Height ◽

Tree Level ◽

Elasticity Analysis ◽

Scale Elasticity ◽

Stem Taper ◽

Product Value ◽

Relationship Of ◽

The Relationship ◽

Tree Characteristics

The establishment of the relationship between tree-level product value and tree characteristics will allow for predicting the potential value of individual trees and a stand directly using tree characteristics. Using statistical and elasticity analysis methods this study examined the relationship of tree-level product value with selected tree characteristics in black spruce (Picea mariana). The study was based a sample of 139 trees from 48-year-old black spruce plantations grown in Ontario, Canada. The sample trees showed large variation in tree characteristics and tree-level product value. Models were developed and compared on the basis of statistics of the estimated and predicted criteria. Results show that the model, including only tree DBH, tree height and stem taper, is the best in describing the relationship of the tree-level product value with tree characteristics. Furthermore, relationships including input-output and interaction factors in the model were analyzed by calculating the elasticity of production and scale and the cross partial derivative of output with respect to the inputs. The analyses indicate that tree DBH has the largest and positive influence on tree-level product value, followed by tree height; however, stem taper has a negative effect on tree-level product value. When tree DBH, tree height and stem taper each increase by 1%, the quantities of output elasticity show 2.53%, 0.64% and -0.37% changes in the product value, respectively; while the scale elasticity shows a 2.81% increase in tree-level product value with a simultaneous 1% change in tree DBH, tree height and stem taper. Results indicate that the model is suitable for predicting tree-level product value using those tree characteristics from forest inventory and also reflects biological behaviour.Key words: black spruce, regression models, elasticity analysis, product value, tree characteristics

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Modelling the Tree Height, Crown Base Height, and Effective Crown Height of Pinus koraiensis Plantations Based on Knot Analysis

Forests ◽

10.3390/f12121778 ◽

2021 ◽

Vol 12 (12) ◽

pp. 1778

Author(s):

Wancai Zhu ◽

Zhaogang Liu ◽

Weiwei Jia ◽

Dandan Li

Keyword(s):

Tree Height ◽

Information Criterion ◽

Mixed Effects ◽

Mixed Effects Model ◽

Pinus Koraiensis ◽

Tree Level ◽

Model Parameters ◽

Crown Height ◽

Crown Base Height ◽

Pruning Intensity

Taking 1735 Pinus koraiensis knots in Mengjiagang Forest Farm plantations in Jiamusi City, Heilongjiang Province as the research object, a dynamic tree height, effective crown height, and crown base height growth model was developed using 349 screened knots. The Richards equation was selected as the basic model to develop a crown base height and effective crown height nonlinear mixed-effects model considering random tree-level effects. Model parameters were estimated with the non-liner mixed effect model (NLMIXED) Statistical Analysis System (SAS) module. The akaike information criterion (AIC), bayesian information criterion (BIC), −2 Log likelihood (−2LL), adjusted coefficient (Ra2), root mean square error (RMSE), and residual squared sum (RSS) values were used for the optimal model selection and performance evaluation. When tested with independent sample data, the mixed-effects model tree effects-considering outperformed the traditional model regarding their goodness of fit and validation; the two-parameter mixed-effects model outperformed the one-parameter model. Pinus koraiensis pruning times and intensities were calculated using the developed model. The difference between the effective crown and crown base heights was 1.01 m at the 15th year; thus, artificial pruning could occur. Initial pruning was performed with a 1.01 m intensity in the 15th year. Five pruning were required throughout the young forest period; the average pruning intensity was 1.46 m. The pruning interval did not differ extensively in the half-mature forest period, while the intensity decreased significantly. The final pruning intensity was only 0.34 m.

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A Merchantable and Total Height Model for Tree Species in Maine

Northern Journal of Applied Forestry ◽

10.1093/njaf/23.4.241 ◽

2006 ◽

Vol 23 (4) ◽

pp. 241-249 ◽

Cited By ~ 1

Author(s):

James A. Westfall ◽

Kenneth M. Laustsen

Keyword(s):

Tree Height ◽

Mixed Effects ◽

Site Quality ◽

Tree Level ◽

Mixed Effects Modeling ◽

Height Prediction ◽

Species Groups ◽

Total Tree ◽

Height Model ◽

Tree Characteristics

Abstract A model for predicting merchantable and total tree height for 18 species groups in Maine is presented. Only tree-level predictor variables are used, so stand-level attributes, such as age and site quality, are not required. A mixed-effects modeling approach accounts for the correlated within-tree measurements. Data-collection protocols encompass situations in which merchantability to a specified top diameter is not attained due to tree characteristics. The advantage of using the height prediction model over taper-derived estimates of merchantable height is demonstrated.

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Comparison of Backpack, Handheld, Under-Canopy UAV, and Above-Canopy UAV Laser Scanning for Field Reference Data Collection in Boreal Forests

Remote Sensing ◽

10.3390/rs12203327 ◽

2020 ◽

Vol 12 (20) ◽

pp. 3327 ◽

Cited By ~ 1

Author(s):

Eric Hyyppä ◽

Xiaowei Yu ◽

Harri Kaartinen ◽

Teemu Hakala ◽

Antero Kukko ◽

...

Keyword(s):

Data Collection ◽

Point Cloud ◽

Laser Scanning ◽

Reference Data ◽

Tree Height ◽

Tree Level ◽

Stem Volume ◽

Point Cloud Data ◽

Cloud Data ◽

Individual Trees

In this work, we compared six emerging mobile laser scanning (MLS) technologies for field reference data collection at the individual tree level in boreal forest conditions. The systems under study were an in-house developed AKHKA-R3 backpack laser scanner, a handheld Zeb-Horizon laser scanner, an under-canopy UAV (Unmanned Aircraft Vehicle) laser scanning system, and three above-canopy UAV laser scanning systems providing point clouds with varying point densities. To assess the performance of the methods for automated measurements of diameter at breast height (DBH), stem curve, tree height and stem volume, we utilized all of the six systems to collect point cloud data on two 32 m-by-32 m test sites classified as sparse (n = 42 trees) and obstructed (n = 43 trees). To analyze the data collected with the two ground-based MLS systems and the under-canopy UAV system, we used a workflow based on our recent work featuring simultaneous localization and mapping (SLAM) technology, a stem arc detection algorithm, and an iterative arc matching algorithm. This workflow enabled us to obtain accurate stem diameter estimates from the point cloud data despite a small but relevant time-dependent drift in the SLAM-corrected trajectory of the scanner. We found out that the ground-based MLS systems and the under-canopy UAV system could be used to measure the stem diameter (DBH) with a root mean square error (RMSE) of 2–8%, whereas the stem curve measurements had an RMSE of 2–15% that depended on the system and the measurement height. Furthermore, the backpack and handheld scanners could be employed for sufficiently accurate tree height measurements (RMSE = 2–10%) in order to estimate the stem volumes of individual trees with an RMSE of approximately 10%. A similar accuracy was obtained when combining stem curves estimated with the under-canopy UAV system and tree heights extracted with an above-canopy flying laser scanning unit. Importantly, the volume estimation error of these three MLS systems was found to be of the same level as the error corresponding to manual field measurements on the two test sites. To analyze point cloud data collected with the three above-canopy flying UAV systems, we used a random forest model trained on field reference data collected from nearby plots. Using the random forest model, we were able to estimate the DBH of individual trees with an RMSE of 10–20%, the tree height with an RMSE of 2–8%, and the stem volume with an RMSE of 20–50%. Our results indicate that ground-based and under-canopy MLS systems provide a promising approach for field reference data collection at the individual tree level, whereas the accuracy of above-canopy UAV laser scanning systems is not yet sufficient for predicting stem attributes of individual trees for field reference data with a high accuracy.

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Influence of Stem Taper on the Yield of Black Spruce Stands and Trees Following Commercial Thinning

Forests ◽

10.3390/f10111024 ◽

2019 ◽

Vol 10 (11) ◽

pp. 1024 ◽

Cited By ~ 1

Author(s):

Manon Vincent ◽

Cornelia Krause ◽

Ahmed Koubaa

Keyword(s):

Treatment Effect ◽

Black Spruce ◽

Growth Increment ◽

Tree Level ◽

Stem Volume ◽

Stand Volume ◽

Commercial Thinning ◽

Volume Increment ◽

Individual Trees ◽

Stem Shape

In this work, we examine the effects of commercial thinning on stand volume and individual stem form in nine naturally regenerated black spruce (Picea mariana (Mill.) B.S.P.) stands. We compared these study sites with controls in the commercial boreal forest of northern Quebec, Canada. At stand level, dendrochronological data provided insight into changes in stand volume ten years after thinning. Analysis of a subsample of six individual trees from each commercially thinned stand and three individual trees from the controls illustrated the role of thinning on stem shape development. Although average volume increased for residual stems in thinned stands slightly more than in the controls (110% versus 106%), the treatment effect stand-level volume increment or stand-level total volume harvested (ten years after treatment) was not statistically significant. Moreover, at tree level, thinning did not significantly affect stem volume increment. However, radial growth increment significantly increased after treatment. Trees from commercially thinned stands showed a significantly higher growth increment along the lower first two-thirds of the stem. Response to thinning at tree level correlated strongly with the size and number of harvested competitors around a residual stem. We conclude that commercial thinning modified wood allocation rather than wood volume and did not affect taper and stem shape. These patterns of post-cutting growth are explained by wood allocation following thinning. After commercial thinning, growth increment is favored at the expense of height growth. As the treatment effect was found at the stem scale rather than at the stand scale, further research is needed in regard to commercial thinning treatments to investigate how to increase productivity at the stand scale.

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Allometric relationships for surface area and dry mass of young Norway spruce aboveground organs

Journal of Forest Science ◽

10.17221/2166-jfs ◽

2008 ◽

Vol 53 (No. 12) ◽

pp. 548-554 ◽

Cited By ~ 16

Author(s):

R. Pokorný ◽

I. Tomášková

Keyword(s):

Surface Area ◽

Norway Spruce ◽

Tree Height ◽

Dry Mass ◽

Tree Level ◽

Stem Volume ◽

Age Classes ◽

Sapwood Area ◽

Needle Age ◽

Leaf Mass

Tree-level allometric functions for a precise predicting of stem, branch and leaf mass and surface area of three needle-shoot age classes were estimated from measurements of crown and stem dimensions in 34 harvested Norway spruce (Picea abies [L.] Karst.) trees. Trees were grown within a 16-years-old stand in the Beskids Mountains. The results showed stem parameters (stem diameter at breast height – dbh, stem volume – Vs and stem sapwood area – SA) to be highly correlated (r > 0.98) with stem mass/area and total aboveground mass of tree. Crown parameters – volume (Cv) and surface area (Ca) were the best predictors for individual branch and needle age-classes mass (r > 0.92) or area (r > 0.85), specifically for mass and surface areas of young branches and needles. dbh most correctly predicted the branch and leaf mass/surface area of older (> 2 years) shoots. The measured parameters: dbh, SA, tree height, crown length, Ca and Cv showed a high dependence on the tree position within the stand (r > –0.81). Thus, these parameters could be modified by silviculture.

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Developing Allometric Equations for Teak Plantations Located in the Coastal Region of Ecuador from Terrestrial Laser Scanning Data

Forests ◽

10.3390/f10121050 ◽

2019 ◽

Vol 10 (12) ◽

pp. 1050 ◽

Cited By ~ 2

Author(s):

Fernando J. Aguilar ◽

Abderrahim Nemmaoui ◽

Alberto Peñalver ◽

José R. Rivas ◽

Manuel A. Aguilar

Keyword(s):

Laser Scanning ◽

Coastal Region ◽

Terrestrial Laser Scanning ◽

Tree Height ◽

Tree Level ◽

Stem Volume ◽

Automatic Data ◽

Allometric Models ◽

Teak Plantations ◽

Tree Stem

Traditional studies aimed at developing allometric models to estimate dry above-ground biomass (AGB) and other tree-level variables, such as tree stem commercial volume (TSCV) or tree stem volume (TSV), usually involves cutting down the trees. Although this method has low uncertainty, it is quite costly and inefficient since it requires a very time-consuming field work. In order to assist in data collection and processing, remote sensing is allowing the application of non-destructive sampling methods such as that based on terrestrial laser scanning (TLS). In this work, TLS-derived point clouds were used to digitally reconstruct the tree stem of a set of teak trees (Tectona grandis Linn. F.) from 58 circular reference plots of 18 m radius belonging to three different plantations located in the Coastal Region of Ecuador. After manually selecting the appropriate trees from the entire sample, semi-automatic data processing was performed to provide measurements of TSCV and TSV, together with estimates of AGB values at tree level. These observed values were used to develop allometric models, based on diameter at breast height (DBH), total tree height (h), or the metric DBH2 × h, by applying a robust regression method to remove likely outliers. Results showed that the developed allometric models performed reasonably well, especially those based on the metric DBH2 × h, providing low bias estimates and relative RMSE values of 21.60% and 16.41% for TSCV and TSV, respectively. Allometric models only based on tree height were derived from replacing DBH by h in the expression DBH2 x h, according to adjusted expressions depending on DBH classes (ranges of DBH). This finding can facilitate the obtaining of variables such as AGB (carbon stock) and commercial volume of wood over teak plantations in the Coastal Region of Ecuador from only knowing the tree height, constituting a promising method to address large-scale teak plantations monitoring from the canopy height models derived from digital aerial stereophotogrammetry.

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Modelling knot morphology as a function of external tree and branch attributes

Canadian Journal of Forest Research ◽

10.1139/cjfr-2012-0365 ◽

2013 ◽

Vol 43 (3) ◽

pp. 266-277 ◽

Cited By ~ 19

Author(s):

E. Duchateau ◽

F. Longuetaud ◽

F. Mothe ◽

C. Ung ◽

D. Auty ◽

...

Keyword(s):

Tree Growth ◽

Pinus Banksiana ◽

Black Spruce ◽

Three Dimensional ◽

Tree Height ◽

Jack Pine ◽

Weibull Function ◽

Data Set ◽

External Branch ◽

Tree Characteristics

Existing models for describing knot morphology are typically based on polynomial functions with parameters that are often not biologically interpretable. Hence, they are difficult to integrate into tree growth simulators due to the limited possibilities for linking knot shape to external branch and tree characteristics. X-ray computed tomography (CT) images taken along the stems of 16 jack pine (Pinus banksiana Lamb.) trees and 32 black spruce (Picea mariana (Mill.) B.S.P.) trees were used to extract the three-dimensional shape of 3450 and 11 276 knots from each species, respectively. Using a nonlinear approach, we firstly fitted a model of knot geometry adapted from a Weibull function. Separate equations were used to describe both the curvature and the diameter of the knot along its pith. Combining these two equations gave an accurate representation of knot shape using only five parameters. Secondly, to facilitate the integration of the resulting model into a tree growth simulator, we extracted the parameters obtained for each knot and modelled them as functions of external branch and tree characteristics (e.g., branch diameter, insertion angle, position in the stem, tree height, and stem diameter). When fitted to a separate data set, the model residuals of the black spruce knot curvature equation were less than 2.9 mm in any part of the knot profile for 75% of the observations. The corresponding value from the diameter equation was 2.8 mm. In jack pine, these statistics increased to 5.4 mm and 3.2 mm, respectively. Overall, the ability to predict knot attributes from external tree- and branch-level variables has the potential to improve the simulation of internal stem properties.

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Combining tree height samples produced by airborne laser scanning and stand management records to estimate plot volume in Eucalyptus plantations

Canadian Journal of Forest Research ◽

10.1139/x11-083 ◽

2011 ◽

Vol 41 (8) ◽

pp. 1649-1658 ◽

Cited By ~ 18

Author(s):

Jari Vauhkonen ◽

Lauri MehtÄtalo ◽

Petteri Packalén

Keyword(s):

Laser Scanning ◽

Tree Height ◽

Small Sample ◽

Airborne Laser Scanning ◽

Tree Level ◽

Stem Volume ◽

Data Set ◽

Stand Management ◽

Tree Detection ◽

Airborne Laser

Regular stand structure and availability of precise silvicultural management data produce a special situation regarding remote sensing based assessments of plantation forests. This study tested the use of stand management records to improve single-tree detection in a Eucalyptus plantation. Combined airborne laser scanning (ALS) and planting distance data were used to detect trees and extract their heights. The extracted heights were used as an input for volume estimation using both existing plot-level functions and new tree-level models. The accuracies were evaluated in a test data set of 191 field reference plots in which the diameters of the Eucalyptus urograndis (E. grandis (Hill) Maiden × E. urophylla S.T. Blake) trees varied from 6 to 41 cm and tree heights varied from 12 to 41 m. The constructed mixed-effects model that predicted stem volume from tree height resulted in a root mean squared error (RMSE) of 68 dm3 (15%) in a cross validation of the modeling data. The tree detection produced estimates of stem number with low bias (i.e., average difference between measured and estimated) and an RMSE of 6% of the mean, whereas plot-level mean and dominant heights were estimated with RMSEs of 1.5 m (5%) and 2 m (6%), respectively, using ALS data alone. The difference of about 60 cm observed between the ALS-based and field-measured dominant height was most likely caused by the penetration of the laser pulses through the canopy. A system of plot-level models that employed a small sample of calibration field data gave RMSEs of 1 m (3%) and 2.2 m2/ha (9%) for site index and basal area, respectively. The plot volume was estimated with an RMSE of 44 m3/ha (12%) at best. A similar residual variation was observed in the volume estimates of an area-based method applied to the same data set. The combined results suggest the feasibility of the proposed methodology in a plantation inventory using ALS data with a density of only 1.5 pulses/m2.

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