Modeling taper and volume of Sal (Shorea robusta Gaertn. f.) trees in the western Terai region of Nepal

Volume and taper equations are used for estimating timber volume and biomass of a tree. Despite their usefulness, precise and site specific equations are still lacking for commercially important tree species in Nepal. The study was carried out at Chandak Chatiya Mahila Community Forest in Bardia district and Lumbini Collaborative Forest of Saljhandi in Rupandehi district in western Terai of Nepal. A destructive sampling method was used and selected fifteen Sal trees (Shorea robusta Gaertn. f.) from Saljhandi (site 1) and eighteen trees from Bagnaha (site 2) randomly to calibrate an individual tree volume and a stem taper function. At first, a non-linear stem taper function was calibrated using stem diameters outside bark at different heights above ground as response variable and D (diameter at breast height), H (total height), h (height of interest) as predictors. Then, effect of crown characteristics on stem taper was evaluated. As stem HCB (height to crown base) was found to affect stem taper, its usefulness in existing stem volume equation was tested. Empirical relationships between V (stem volume) as a response variable and D, H, HCB and sites in Bardia and Rupandehi districts as predictors were established using a linear mixed modeling approach. Our result showed that, instead of H, use of HCB in stem volume equation increased model prediction accuracy and reduced prediction bias. Applicability of the suggested models for predicting individual S. robusta tree volume and stem taper is discussed. Banko JanakariA Journal of Forestry Information for Nepal Special Issue No. 4, 2018, Page: 76-83

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Accuracy of common stem volume formulae using terrestrial photogrammetric point clouds: a case study with savanna trees in Benin

Journal of Forestry Research ◽

10.1007/s11676-021-01333-9 ◽

2021 ◽

Author(s):

Hospice A. Akpo ◽

Gilbert Atindogbé ◽

Maxwell C. Obiakara ◽

Arios B. Adjinanoukon ◽

Madaï Gbedolo ◽

...

Keyword(s):

Point Clouds ◽

Stem Volume ◽

Individual Tree ◽

Volume Calculation ◽

Tropical Regions ◽

Solid Of Revolution ◽

Taper Function ◽

Geometric Solids ◽

Traditional Approaches ◽

Tree Stem

AbstractRecent applications of digital photogrammetry in forestry have highlighted its utility as a viable mensuration technique. However, in tropical regions little research has been done on the accuracy of this approach for stem volume calculation. In this study, the performance of Structure from Motion photogrammetry for estimating individual tree stem volume in relation to traditional approaches was evaluated. We selected 30 trees from five savanna species growing at the periphery of the W National Park in northern Benin and measured their circumferences at different heights using traditional tape and clinometer. Stem volumes of sample trees were estimated from the measured circumferences using nine volumetric formulae for solids of revolution, including cylinder, cone, paraboloid, neiloid and their respective fustrums. Each tree was photographed and stem volume determined using a taper function derived from tri-dimensional stem models. This reference volume was compared with the results of formulaic estimations. Tree stem profiles were further decomposed into different portions, approximately corresponding to the stump, butt logs and logs, and the suitability of each solid of revolution was assessed for simulating the resulting shapes. Stem volumes calculated using the fustrums of paraboloid and neiloid formulae were the closest to reference volumes with a bias and root mean square error of 8.0% and 24.4%, respectively. Stems closely resembled fustrums of a paraboloid and a neiloid. Individual stem portions assumed different solids as follows: fustrums of paraboloid and neiloid were more prevalent from the stump to breast height, while a paraboloid closely matched stem shapes beyond this point. Therefore, a more accurate stem volumetric estimate was attained when stems were considered as a composite of at least three geometric solids.

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COMPATIBILITY BETWEEN THE STEM VOLUME AND TAPER EQUATIONS VOLUME FOR BLACK WATTLE TREES

FLORESTA ◽

10.5380/rf.v50i3.63881 ◽

2020 ◽

Vol 50 (3) ◽

pp. 1518

Author(s):

Marcos Behling ◽

Henrique Soares Koehler ◽

Alexandre Behling

Keyword(s):

Traditional Approach ◽

Stem Volume ◽

System Of Equations ◽

Data Set ◽

Taper Function ◽

Black Wattle ◽

Taper Equations ◽

Volume Estimates ◽

Forest Engineering

A system of equations widely used in Forest Engineering by the international community of researchers consists of a combination of a volumetric function and a taper function, with the purpose of making volume estimates compatible. When using the volume function and the taper function in a system, the result of the volume estimated by the two functions should be compatible, meaning that the volume estimated by the volumetric function should not differ from the volume obtained by integrating the taper function. Thus, the purpose of this paper was to develop and present the procedures of a system of equations to make volume estimates from both volume and taper equations compatible, and then compare it to the traditional approach, which is used in forestry companies. The procedures proposed were applied to a data set on the Acacia mearnsii De Wild. (black wattle) at sites where the plantation of this species is concentrated in the state of Rio Grande do Sul. The data set included 343 trees ranging from 5 to 10.75 years of age. It was noted that the lack of volume compatibility, in absolute terms, grows exponentially with the size of the tree. The quality of the estimates using the system of compatible equations did not differ from those obtained from the traditional model, therefore, the former is preferable. Furthermore, it was noted that the residuals from the volume and taper equations are correlated, which suggests that the system of equations be fitted simultaneously.

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Stem Taper and Volume of Managed Red Alder

Western Journal of Applied Forestry ◽

10.1093/wjaf/22.1.61 ◽

2007 ◽

Vol 22 (1) ◽

pp. 61-66 ◽

Cited By ~ 5

Author(s):

David Hibbs ◽

Andrew Bluhm ◽

Sean Garber

Keyword(s):

Pacific Northwest ◽

Tree Height ◽

Data Set ◽

Individual Tree ◽

Red Alder ◽

Volume Table ◽

Taper Function ◽

Independent Evaluation ◽

The Pacific ◽

Taper Equations

Abstract Ataper equation and a volume table are presented for red alder (Alnus rubra Bong.) trees grown in plantations. Fourteen diameter measurements from each of 234 trees were collected from nine plantations throughout the Pacific Northwest. Diameter inside bark (dib) along the stemwas fitted to a variable exponent model form. Individual tree merchantable volume was then estimated as volume inside bark by integrating the taper function from 6 in. (stump height) to the height at a 5-in. (diameter outside bark) top. Incorporating two easily measured tree variables—dbhand total tree height—provided an accurate fit. Model results and the use of an independent evaluation data set of plantation-grown trees indicated that the model presented here was a better predictor of dib in managed stands than previously published red alder taper equations. Thisequation provides reliable dib and merchantable volume predictions and is an improvement over previous red alder volume and taper equations.

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Compatible taper function for Scots pine plantations in northwestern Spain

Canadian Journal of Forest Research ◽

10.1139/x06-008 ◽

2006 ◽

Vol 36 (5) ◽

pp. 1190-1205 ◽

Cited By ~ 55

Author(s):

Ulises Diéguez-Aranda ◽

Fernando Castedo-Dorado ◽

Juan Gabriel Álvarez-González ◽

Alberto Rojo

Keyword(s):

Scots Pine ◽

Model Development ◽

Individual Tree ◽

Stand Volume ◽

Taper Function ◽

Northwestern Spain ◽

Volume Equation ◽

Taper Equation ◽

Volume Equations

A compatible system for estimation of individual tree volume was developed for Scots pine (Pinus sylvestris L.) in northwestern Spain. The system comprises a merchantable volume equation, a total volume equation, and a taper function. The use of the volume equation allows rapid estimation of tree volume, and stand volume by summing individual tree volumes, which is equal to the volume obtained by integrating the taper equation. The volume equation is very easy to use and is therefore preferred when classification of the products by merchantable sizes is not required. Data from 228 destructively sampled trees were used for model development. Fourteen compatible volume equations were evaluated, 13 of these equations were taken from the available literature, and the other was developed in the present study. A modified second-order continuous autoregressive error structure was used to correct the autocorrelation of the hierarchical data used. The model developed by Fang et al. (Z. Fang, B.E. Borders, and R.L. Bailey. 2000. For. Sci. 46: 112) best described the data. There model is therefore recommended for the estimation of diameter at a specific height, merchantable volume, and total volume of Scots pine stems in the area of study.

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Comparison of stem taper equations for eight major tree species in the Spanish Plateau

Forest Systems ◽

10.5424/fs/2015243-06229 ◽

2015 ◽

Vol 24 (3) ◽

pp. e034 ◽

Cited By ~ 9

Author(s):

Francisco Rodríguez ◽

Iñigo Lizarralde ◽

Felipe Bravo

Keyword(s):

Goodness Of Fit ◽

Inflection Point ◽

Cross Validation ◽

Central Spain ◽

First Order ◽

Stem Taper ◽

Hardwood Species ◽

Taper Function ◽

Taper Equations ◽

Order Continuous

Aim of study: A stem taper function and a compatible merchantable volume system are compared to evaluate which provides a better description of the stem profile for the main species in central Spain.Area of study: This research was carried out in the region of Castile-Leon, located in Central Spain.Material and Methods: A total of 6,357 trees were selected for destructive sampling. All models were fitted using a first-order continuous autoregressive error structure to address the problem of autocorrelation.Main results: In terms of accuracy, the root mean square error (RMSE) in both models ranged from 0.75 to 2.72 depending on the species analyzed, presenting values similar to those reported in other studies. Small differences in the goodness-of-fit for both procedures were also found, and the Stud model provided better accuracy for 6 of the 8 species studied, with RMSE reductions of 0.5% to 8.6%. The RMSE obtained in the cross-validation phase was on average 1.22 times higher than what was obtained in the fitting phase.Research highlights: The non-linear extra sum of squares method indicated that the stem taper differs among the five softwood species and three hardwood species. In hardwoods, the first inflection point is lower than in softwoods (at around 5%) and the second inflection point is higher (at around 85%) than those of softwoods.Keywords: taper function; volume system; Central Spain; softwoods; hardwoods.

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The Estimation of Stem Volume for Pinus thunbergii by Coast using Kozak’s Stem Taper Model in Korea

The Journal of Korean Island ◽

10.26840/jki.29.4.225 ◽

2017 ◽

Vol 29 (4) ◽

pp. 225-244 ◽

Cited By ~ 2

Author(s):

Yeongmo Son ◽

Jinteak Kang ◽

Juhyeon Jeon ◽

Chiung Ko

Keyword(s):

Pinus Thunbergii ◽

Stem Volume ◽

Stem Taper ◽

Taper Model

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Tree growth as affected by stem and crown structure

Trees ◽

10.1007/s00468-021-02092-0 ◽

2021 ◽

Author(s):

Hans Pretzsch

Keyword(s):

Tree Growth ◽

Scaling Theory ◽

Tree Age ◽

Stem Volume ◽

Projection Area ◽

Metabolic Scaling ◽

Crown Structure ◽

The Future ◽

Metabolic Scaling Theory ◽

Crown Characteristics

Abstract Key message Prediction of tree growth based on size or mass as proposed by the Metabolic Scaling Theory is an over-simplification and can be significantly improved by consideration of stem and crown morphology. Tree growth and metabolic scaling theory, as well as corresponding growth equations, use tree volume or mass as predictors for growth. However, this may be an over-simplification, as the future growth of a tree may, in addition to volume or mass, also depend on its past development and aspects of the current inner structure and outer morphology. The objective of this evaluation was to analyse the effect of selected structural and morphological tree characteristics on the growth of common tree species in Europe. Here, we used eight long-term experiments with a total of 24 plots and extensive individual measurements of 1596 trees in monospecific stands of European beech (Fagus sylvatica L.), Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and sessile oak (Quercus petraea (Matt.) Liebl.). Some of the experiments have been systematically surveyed since 1870. The selected plots represent a broad range of stand density, from fully to thinly stocked stands. We applied linear mixed models with random effects for analysing and modelling how tree growth and productivity are affected by stem and crown structure. We used the species-overarching relationship $$\mathrm{iv}={{a}_{0}\times v}$$ iv = a 0 × v between stem volume growth, $$\mathrm{iv}$$ iv and stem volume, $$v,$$ v , as the baseline model. In this model $${a}_{0}$$ a 0 represents the allometric factor and α the allometric exponent. Then we included tree age, mean stem volume of the stand and structural and morphological tree variables in the model. This significantly reduced the AIC; RMSE was reduced by up to 43%. Interestingly, the full model estimating $$\mathrm{iv}$$ iv as a function of $$v$$ v and mean tree volume, crown projection area, crown ratio and mean tree ring width, revealed a $$\alpha \cong 3/4$$ α ≅ 3 / 4 scaling for the relationship between $$\mathrm{iv}\propto {v}^{\alpha }$$ iv ∝ v α . This scaling corresponded with Kleiber’s rule and the West-Brown-Enquist model of the metabolic scaling theory. Simplified approaches based on stem diameter or tree mass as predictors may be useful for a rough estimation of stem growth in uniform stands and in cases where more detailed predictors are not available. However, they neglect other stem and crown characteristics that can have a strong additional effect on the growth behaviour. This becomes of considerable importance in the heterogeneous mixed-species stands that in many countries of the world are designed for forest restoration. Heterogeneous stand structures increase the structural variability of the individual trees and thereby cause a stronger variation of growth compared with monocultures. Stem and crown characteristics, which may improve the analysis and projection of tree and stand dynamics in the future forest, are becoming more easily accessible by Terrestrial laser scanning.

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Variance reduction in Ueno's method and cylinder sampling for forest volume estimation

Canadian Journal of Forest Research ◽

10.1139/x95-193 ◽

1995 ◽

Vol 25 (11) ◽

pp. 1783-1794 ◽

Cited By ~ 3

Author(s):

Thomas B. Lynch

Keyword(s):

Computer Simulation ◽

Variance Reduction ◽

Volume Estimation ◽

Critical Height ◽

Volume Estimate ◽

Individual Tree ◽

Stand Volume ◽

Reduction Techniques ◽

Antithetic Variates ◽

Volume Equation

Three basic techniques are proposed for reducing the variance of the stand volume estimate provided by cylinder sampling and Ueno's method. Ueno's method is based on critical height sampling but does not require measurement of critical heights. Instead, a count of trees whose critical heights are less than randomly generated heights is used to estimate stand volume. Cylinder sampling selects sample trees for which randomly generated heights fall within cylinders formed by tree heights and point sampling plot sizes. The methods proposed here for variance reduction in cylinder sampling and Ueno's method are antithetic variates, importance sampling, and control variates. Cylinder sampling without variance reduction was the most efficient of 12 methods compared in computer simulation that used estimated measurement times. However, cylinder sampling requires knowledge of a combined variable individual tree volume equation. Of the three variance reduction techniques applied to Ueno's method, antithetic variates performed best in computer simulation.

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Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters

Forests ◽

10.3390/f12070913 ◽

2021 ◽

Vol 12 (7) ◽

pp. 913

Author(s):

Serajis Salekin ◽

Cristian Higuera Catalán ◽

Daniel Boczniewicz ◽

Darius Phiri ◽

Justin Morgenroth ◽

...

Keyword(s):

Measurement Techniques ◽

Principal Component ◽

Climatic Conditions ◽

Modern Times ◽

Taper Function ◽

Complex Functions ◽

Artificial Neural Network Ann ◽

Species Specific ◽

Simple Equations ◽

Taper Equations

Taper functions are important tools for forest description, modelling, assessment, and management. A large number of studies have been conducted to develop and improve taper functions; however, few review studies have been dedicated to addressing their development and parameters. This review summarises the development of taper functions by considering their parameterisation, geographic and species-specific limitations, and applications. This study showed that there has been an increase in the number of studies of taper function and contemporary methods have been developed for the establishment of these functions. The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times. Early taper functions included polynomial, sigmoid, principal component analysis (PCA), and linear mixed functions, while contemporary machine learning (ML) approaches include artificial neural network (ANN) and random forest (RF). Further analysis of the published literature also shows that most of the studies of taper functions have been carried out in Europe and the Americas, meaning most taper equations are not specifically applicable to tropical tree species. Developing well-conditioned taper functions requires reducing the variation due to species, measurement techniques, and climatic conditions, among other factors. The information presented in this study is important for understanding and developing taper functions. Future studies can focus on developing better taper functions by incorporating emerging remote sensing and geospatial datasets, and using contemporary statistical approaches such as ANN and RF.

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Comprehensive yield model for plantation teak in Panama

Silva Fennica ◽

10.14214/sf.10309 ◽

2020 ◽

Vol 54 (5) ◽

Author(s):

Petteri Seppänen ◽

Antti Mäkinen

Keyword(s):

Input Parameter ◽

Large Diameter ◽

Measurement Data ◽

Growth And Yield ◽

Tree Level ◽

Stem Volume ◽

Yield Model ◽

Individual Tree ◽

Support Tool ◽

Volume Models

The purpose of this study was to prepare a comprehensive, computerized teak ( L.f) plantation yield model system that can be used to describe the forest dynamics, predict growth and yield and support forest planning and decision-making. Extensive individual tree and permanent sample plot data were used to develop tree-level volume models, taper curve models and stand-level yield models for teak plantations in Panama. Tree volume models were satisfactorily validated against independent measurement data and other published models. Tree height as input parameter improved the stem volume model marginally. Stand level yield models produced comparable harvest volumes with models published in the literature. Stand level volume product outputs were found like actual harvests with an exception that the models marginally underestimate the share of logs in very large diameter classes. The kind of comprehensive model developed in this study and implemented in an easy to use software package provides a very powerful decision support tool. Optimal forest management regimes can be found by simulating different planting densities, thinning regimes and final harvest ages. Forest practitioners can apply growth and yield models in the appropriate stand level inventory data and perform long term harvest scheduling at property level or even at an entire timberland portfolio level. Harvest schedules can be optimized using the applicable financial parameters (silviculture costs, harvesting costs, wood prices and discount rates) and constraints (market size and operational capacity).Tectona grandis

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