iForest - Biogeosciences and Forestry


Modelling taper and stem volume considering stand density in Eucalyptus grandis and Eucalyptus dunnii

Andrés Hirigoyen (1)   , Rafael Navarro-Cerrillo (2), Maurizio Bagnara (3), Jorge Franco (4), Fernando Requin (1), Cecilia Rachid-Casnati (1)

iForest - Biogeosciences and Forestry, Volume 14, Issue 2, Pages 127-136 (2021)
doi: https://doi.org/10.3832/ifor3604-014
Published: Mar 16, 2021 - Copyright © 2021 SISEF

Research Articles

Eucalyptus grandis and Eucalyptus dunnii are the most planted tree species in Uruguay. Anticipating information about the quantity and quality of wood is important for managing intensive forest plantation. The estimate of merchantable and total wood volume is an essential tool in forest planning and management. The aim of this study was to evaluate four systems of taper and merchantable volume that consisted in a taper, a merchantable volume and a total tree volume function. A modified second-order continuous autoregressive error structure corrected the inherent serial autocorrelation of different observations in one tree. Taper and volume equations were fitted simultaneously after autocorrelation correction by full information maximum likelihood method. The segmented system proposed by Fang et al. (2000) produced the best fit as it explained more than 98% of the taper, merchantable volume and total volume variability for both species. In addition, precision of the segmented system was compared with and without incorporating stand density as a variable. Results of this analysis showed that for E. grandis, the predictive accuracy of the model was improved by including the stand density variable, whereas for E. dunnii this variable was not statistically significant. This modelling framework provides an improvement in taper and tree volume predictions for E. dunnii and E. grandis in Uruguay. The possibilities offered by this methodology could be of interest for its application in countries where fast growing plantations are managed.


Compatible Systems, Taper, Simultaneous Estimation, Intensive Silviculture, Eucalyptus

Authors’ address

Andrés Hirigoyen 0000-0002-2116-1095
Fernando Requin
Cecilia Rachid-Casnati 0000-0002-8621-7061
National Institute of Agricultural Research (INIA) Tacuarembó, Ruta 5 km 386, Tacuarembó (Uruguay)
Rafael Navarro-Cerrillo 0000-0003-3470-8640
Department of Forestry Engineering, Laboratory of Silviculture, Dendrochronology and Climate Change, DendrodatLab- ERSAF, University of Cordoba, Campus de Rabanales, Crta. IV, km. 396, E-14071 Córdoba (Spain)
Maurizio Bagnara 0000-0002-9004-7886
Senckenberg Biodiversity and Climate Research Centre (SBiK-F), Senckenberganlage 25, D-60325 Frankfurt am Main (Germany)
Jorge Franco
University of the Republic, Faculty of Agronomy, Paysandú (Uruguay)

Corresponding author

Andrés Hirigoyen


Hirigoyen A, Navarro-Cerrillo R, Bagnara M, Franco J, Requin F, Rachid-Casnati C (2021). Modelling taper and stem volume considering stand density in Eucalyptus grandis and Eucalyptus dunnii. iForest 14: 127-136. - doi: 10.3832/ifor3604-014

Academic Editor

Angelo Rita

Paper history

Received: Jul 31, 2020
Accepted: Jan 15, 2021

First online: Mar 16, 2021
Publication Date: Apr 30, 2021
Publication Time: 2.00 months

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Ahnlund K, Ulvcrona T, Nilsson U, Lundmark T (2014)
Stand density and fertilization effects on aboveground allocation patterns and stem form of Pinus sylvestris in young stands. Scandinavian Journal of Forest Research 29: 197-209.
CrossRef | Gscholar
Anderson-Sprecher R (1994)
Model comparisons and r2. American Statistician 48: 113-117.
CrossRef | Gscholar
Belsley DA (1991)
Conditioning diagnostics: collinearity and weak data in regression. Operational Research Society 44: 88-88.
Bi H (2000)
Trigonometric variable-form taper equations for Australian eucalypts. Forest Science 46: 397-409.
Online | Gscholar
Calama R, Montero G (2006)
Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: a multilevel random components approach. Investigación Agraria: Sistemas y Recursos Forestales 1 (5): 24-41.
CrossRef | Gscholar
Castaño JP, Giménez A, Ceroni M, Furest J, Aunchayna R, Bidegain M (2011)
Caracterización agroclimática del Uruguay 1980-2009. [Agroclimatic characterization of Uruguay 1980-2000]. Serie Técnica INIA 193. Montevideo, Uruguay, pp. 33. [in Spanish]
Clutter J (1980)
Development of taper functions from variable-top merchantable volume equations. Forest Science 26: 117-120.
Online | Gscholar
Diéguez-Aranda U, Castedo-Dorado F, Alvarez-González JG, Rojo A (2006)
Compatible taper function for Scots pine plantations in northwestern Spain. Canadian Journal of Forest Research 36: 1190-1205.
CrossRef | Gscholar
Dufour JM, Dagenais MG (1985)
Durbin-Watson tests for serial correlation in regressions with missing observations. Journal of Econometrics 27: 371-381.
CrossRef | Gscholar
Fang Z, Borders BE, Bailey RL (2000)
Compatible volume-taper models for loblolly and slash pine based on a system with segmented-stem form factors. Forest Science 46: 1-12.
Online | Gscholar
Garber SM, Maguire DA (2003)
Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures. Forest Ecology and Management 179: 507-522.
CrossRef | Gscholar
Gomat HY, Deleporte P, Moukini R, Mialounguila G, Ognouabi N, Saya AR, Vigneron P, Saint-Andre L (2011)
What factors influence the stem taper of Eucalyptus: growth, environmental conditions, or genetics? Annals of Forest Science 68 (1): 109-120.
CrossRef | Gscholar
Gray HR (1956)
The form and taper of forest-tree stems. Imperial Forestry Institute, University of Oxford, UK, pp. 79.
Hernández-Ramos J, Hernández-Ramos A, García-Magaña JDJ, García-Cuevas X, García-Espinoza GG, Muñoz Flores HJ, Olvera-Delgadillo EH (2017)
Sistema compatible de ahusamiento-volumen comercial para plantaciones de Pinus greggii Engelm. en Hidalgo, México [Compatible tree taper and volume system for commercial plantations of Pinus greggii Engelm in Hidalgo, Mexico]. Revista Mexicana de Ciencias Forestales 8: 59-70. [in Spanish]
CrossRef | Gscholar
Hirigoyen A, Franco J, Diéguez-Aranda U (2018)
Modelo dinámico de rodal para Eucalyptus globulus (L.) en Uruguay [Dynamic stand model for Eucalyptus globulus (L.) in Uruguay]. Agrociencia Uruguay 22: 63-80. [in Spanish]
CrossRef | Gscholar
Jacobs M, Rais A, Pretzsch H (2020)
Analysis of stand density effects on the stem form of Norway spruce trees and volume miscalculation by traditional form factor equations using terrestrial laser scanning (TLS). Canadian Journal of Forest Research 50: 51-64.
CrossRef | Gscholar
Kirschen RH, O’Higgins EA, Lee RT (2000)
The Royal London space planning: an integration of space analysis and treatment planning. American Journal of Orthodontics and Dentofacial Orthopedics 118: 456-461.
CrossRef | Gscholar
Kozak A, Munro DD, Smith JHG (1969)
Taper functions and their application in forest inventory. The Forestry Chronicle 45: 278-283.
CrossRef | Gscholar
Kozak (1988)
A variable-exponent taper equation. Canadian Journal of Forest Research 18: 1363-1368.
CrossRef | Gscholar
Kozak A (2004)
My last words on taper equations. Forestry Chronicle 80: 507-515.
CrossRef | Gscholar
Lindstrom MJ, Bates DM (1990)
Nonlinear mixed effects models for repeated measures data. Biometrics 46 (3): 673.
CrossRef | Gscholar
Liu Y, Yue C, Wei X, Blanco JA, Trancoso R (2020)
Tree profile equations are significantly improved when adding tree age and stocking degree: an example for Larix gmelinii in the Greater Khingan Mountains of Inner Mongolia, northeast China. European Journal of Forest Research 139: 443-458.
CrossRef | Gscholar
Martin AJ (1981)
Taper and volume equations for selected Appalachian hardwood species. Research Paper NE-490, USDA Forest Service, Northeastern Forest Experiment Station, Broomall, PA, USA, pp. 22.
Online | Gscholar
Max T, Burkhart HE (1976)
Segmented polynomial regression applied to taper equations. Forest Science 22: 283-289.
Online | Gscholar
Methol R (2008)
SAG Eucalyptus: sistema de apoyo a la gestión de Eucalyptus orientadas a la producción de celulosa en Uruguay [SAG Eucalyptus: Eucalyptus management support system aimed at the production of cellulose in Uruguay]. INIA Serie Técnica 173, Montevideo, Uruguay, pp. 26. [in Spanish]
Mora B, Wulder MA, White JC, Hobart G (2013)
Modeling stand height, volume, and biomass from very high spatial resolution satellite imagery and samples of airborne LIDAR. Remote Sensing 5: 2308-2326.
CrossRef | Gscholar
Myers RH (1990)
Classical and modern regression with applications. Duxbury press, Belmont, CA, USA, vol. 2, pp. 473.
Online | Gscholar
Neter J, Kutner MH, Nachtsheim CJ, Wasserman W (1996)
Applied linear statistical models. Irwin, Chicago, IL, USA, pp. 318.
Ozçelik R, Göçeri MF (2015)
Compatible merchantable stem volume and taper equations for eucalyptus plantations in the eastern Mediterranean region of Turkey. Turkish Journal of Agriculture and Forestry 39: 851-863.
CrossRef | Gscholar
Parresol BR (1993)
Modeling multiplicative error variance - An example predicting tree diameter from stump dimensions in bald cypress. Forest Science 39: 670-679.
Online | Gscholar
Picard RR, Cook RD (1984)
Cross-validation of regression models. Journal of the American Statistical Association 79 (387): 575-583.
CrossRef | Gscholar
Poudel KP, Cao QV (2013)
Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. Forest Science 59: 243-252.
CrossRef | Gscholar
PROBIO (2015)
Mejoramiento en la calidad de la información vinculada con la utilización de la biomasa forestal [Improvement in the quality of information related to the use of forest biomass]. Producción de Electricidad a partir de Biomasa - PROBIO, Montevideo, Uruguay, pp. 157. [in Spanish]
Prodan M, Peters R, Cox F, Real P (1997)
Mensura Forestal [Forest Measurement]. GTZ/IICA, Serie Investigación y Educación en Desarrollo Sostenible, San José, Costa Rica. pp. 561. [in Spanish]
Rachid-Casnati C, Mason E, Woollons R, Resquin F (2014)
Volume and taper equations for P. taeda (L.) and E. grandis (Hill ex. Maiden). Agrociencia Uruguay 18: 47-60.
Online | Gscholar
SAS Institute (2004)
SAS/ETS 9.1 user’s guide. SAS Institute Inc., Cary, NY, USA, pp. 4420.
SAS Institute (2012)
SAS/STAT user’s guide, version 9.1. SAS Institute Inc., Cary, NY, USA, pp. 128.
Schumacher F, Hall F (1933)
Logaritmic expression of timber-tree volume. Journal of Agricultural Research 47: 719-734.
Sharma M, Oderwald RG (2001)
Dimensionally compatible volume and taper equations. Canadian Journal of Forest Research 31: 797-803.
CrossRef | Gscholar
Sharma M, Zhang SY (2004)
Variable-exponent taper equations for jack pine, black spruce, and balsam fir in eastern Canada. Forest Ecology and Management 198 (1-3): 39-53.
CrossRef | Gscholar
Sharma M, Parton J (2009)
Modeling stand density effects on taper for jack pine and black spruce plantations using dimensional analysis. Forest Science 55: 268-282.
Online | Gscholar
Spurr S (1954)
Simplified computation of volume and growth. Journal of Forestry 52: 914-922.
Online | Gscholar
Tamarit Urías JC, De Los Santos Posadas HM, Aldrete A, Valdez Lazalde JR, Ramírez Maldonado H, Guerra De La Cruz V (2014)
Sistema de cubicación para árboles individuales de Tectona grandis L.f. mediante funciones compatibles de ahusamiento-volumen [Volume estimation system for individual Tectona grandis L.f. trees through compatible taper/volume functions]. Revista Mexicana de Ciencias Forestales 5: 58-74. [in Spanish]
CrossRef | Gscholar
Tang X, Pérez-Cruzado C, Fehrmann L, Alvarez-González JG, Lu Y, Kleinn C (2016)
Development of a compatible taper function and stand-level merchantable volume model for Chinese fir plantations. PLoS One 11 (1): e0147610.
CrossRef | Gscholar
Teshome T (2011)
Compatible volume-taper equations for predicting merchantable volume to variable merchantable limits for Cupressus lusitanica, Ethiopia. SINET: Ethiopian Journal of Science 28: 15-22.
CrossRef | Gscholar
Vanclay JK, Skovsgaard P (1997)
Evaluating forest growth models. Ecological Modelling 98: 1-12.
CrossRef | Gscholar
Zimmerman DL, Núñez-Antón V (2001)
Parametric modelling of growth curve data: an overview. Test 10 (1): 1-73.
CrossRef | Gscholar

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