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

  • Francisco Rodríguez föra forest technologies. Soria.
  • Iñigo Lizarralde föra forest technologies. Soria.
  • Felipe Bravo Sustainable Forest Management Research Institute University of Valladolid-INIA.


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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Adame P, Hynynen J, Cañellas I, del Río M, 2008. Individual-tree diameter growth model for rebollo oak (Quercus pyrenaica Willd.) coppices. For Ecol Manage 255: 1011–1022.

Barrio-Anta M, Diéguez-Aranda U, Castedo-Dorado F, Álvarez-González JG, Gadow Kv, 2007a. Merchantable volume system for pedunculate oak in northwestern Spain Ann For Sci 64(5): 511-520.

Barrio-Anta M, Sixto H, Cañellas I, González-Antoñanzas F, 2007b. Sistema de cubicación con clasificación de productos para plantaciones de Populus x euramericana (Dode) Guinier cv. 'I-214' en la meseta norte y centro de España. Invest Agrar: Sist Recur For 16(1): 65-75.

Bates DM, Watts DG, 1988. Nonlinear Regression Analysis and Its Applications.

Bi H, 2000. Trigonometric variable-form taper equations for Australian eucalyptus. For Sci 46: 397–409.

Bravo F, Álvarez-González JG, Del Río M, Barrio-Anta M, Bonet JA, Bravo-Oviedo A, Calama R, Castedo-Dorado F, Crecente-Campo F, Condés, et al., 2011. Growth And Yield Models In Spain: Historical Overview, Contemporary Examples And Perspectives. Forest Systems 20(2): 315-328.

Burkhart H, Tomé M, 2012. Modeling Forest Trees and Stands. Springer Ed. 1st Edition., 547 pp.

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. Invest Agr Sist Recur For 15(1): 24-41

Cao QV, Burkhart HE, Max TA, 1980. Evaluations of two methods for cubic-foot volume prediction of loblolly pine to any merchantable limit. For Sci 26: 71–80.

Carvalho JP, Parresol BR, 2005. A site model for Pyrenean oak (Quercus pyrenaica) stands using a dynamic difference equation. Can J For Res 35: 93-99.

Clutter JL, 1980. Development of taper functions from variable-top merchantable volume equations, For Sci 26: 117–120.

Corral-Rivas JJ, Diéguez-Aranda U, Corral S, Castedo-Dorado F, 2007. A merchantable volume system for major pine species in El Salto, Durango (Mexico). For Ecol Manage 238(1-3): 118-129.

Crecente-Campo F, Rojo A, Diéguez-Aranda U, 2009. A merchantable volume system for Pinus sylvestris L. in the major mountain ranges of Spain. Ann For Sci 66: 808-820.

Daquitaine R, Saint-Andre L, Leban JM, 1999. Product properties prediction - improved utilisation in the forestry-wood chain applied on spruce sawnwood: Modelling stem properties distribution. Final Report sub-task A2.1. Nancy.

Diéguez-Aranda U, Castedo F, Álvarez JG, Rojo A, 2006. Compatible taper function for Scots pine plantations in northwestern Spain. Can J For Res 36: 1190–1205.

Fang Z, Borders BE, Bailey RL, 2000. Compatible volume-taper models for loblolly and slash pine based on a system with segmentedstem form factors. For Sci 46: 1–12.

Fonweban J, Gardiner B, Macdonald E, Auty D, 2011. Taper functions for Scots pine (Pinus sylvestris, L.) and Sitka spruce (Picea sitchensis (Bong.) Carr.) in Northern Britain. Forestry, 84(1): 49-60.

Garber SM, Maguire DA, 2003. Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures. For Ecol Manage 179: 507–522.

Gregoire TG, Schabenberger O, Barrett JP, 1995. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Can J For Res 25: 137–156.

Karlsson A, Albrektson A, Elfving B, Fries C, 2002. Development of Pinus sylvestris main stems following three different precommercial thinning methods in a mixed stand. Scand J Forest Res 17(3): 256–262.

Kozak A, Smith JHG, 1993. Standards for evaluating taper estimating systems. For Chron 69: 438–444.

Kozak A, 1997. Effects of multicollinearity and autocorrelation on the variable-exponent taper functions. Can J For Res 27: 619–629.

Laasasenaho J, Melkas T, Alden S, 2005. Modeling bark thickness of Picea abies with taper curves. For Ecol Manage 206: 35-47.

Lappi J, 1986. Mixed linear models for analyzing and predicting stem form variation of Scots pine. Communicationes Instituto Forestalis Fenniae 134: 1–69.

Menéndez-Miguélez M, Canga E, Alvarez-Alvarez P, Majada J, 2014. Stem taper function for sweet chestnut (Castanea sativa Mill.) coppice stands in northwest Spain. Ann For Sci 71(7): 761-770.

Meredieu C, 1998. Croissance et branchaison du Pin laricio (Pinus nigra Arnold ssp. Laricio (Poiret) Maire). Elaboration et évaluation d'un système de modèles pour la prévision de caractéristiques des arbres et du bois. Thèse de Doctorat, Université Claude.

Newnham RM, 1992. Variable-Form Taper Functions for Four Alberta Tree Species. Can J For Res 22: 210-223.

Petersson H, 1999. Biomassafunktioner för trädfunktioner av tall, gran och björk i Sverige. Arbetsrapport 59. Department of Forest Resource Management and Geomatics, Swedish University of Agricultural Science, Umea.

Roda JM, 2001. Form function for the 'I-214' poplar merchantable stem (Populus x euramericana (Dode) Guinier cv cultivar 'I-214'). Ann For Sci 58: 77-87.

Rodríguez F, Broto M, Cantero A, 2004 Aplicación del programa "Cubica" a distintos regímenes de gestión del pino radiata en el País Vasco. Cuadernos Sociedad Española Ciencias Forestales (18):193-198.

Rodríguez F, Pemán J, Aunós A, 2010. A reduced growth model based on stand basal area. A case for hybrid poplar plantations in northeast Spain. For Eco Man 259: 2093-2102.

Rojo A, Perales X, Sánchez-Rodríguez F, Álvarez-González JG, Von Gadow K, 2005. Stem taper functions for maritime pine (Pinus pinaster Ait.) in Galicia (Northwestern Spain). Eur J Forest Res 124: 177–186.

SAS Institute Inc., 2010a. SAS/STAT® 9.2 User's Guide, Second Edition. Available at: [last revised on February 3, 2010].

SAS Institute Inc., 2010b. SAS/ETS®9.2 User's Guide. Available at: [last revised on April 16, 2010].

Skog KE, Nicholson GA, 1998. Carbon cycling through wood products: the role of wood and paper products in carbon sequestration. Forest Products Journal 48:75-86.

Stoltze P, 2000. Overenstemmende stammemasseog stammesidefunktioner for bøg i Danmark. Ministy of Environment and Energy. Danish Forest and Landscape Research Institute. Working report.

Tarp-Johansen MJ, Skovsgaard JP, Madsen SF, Johannsen VK, Skovgaard I, 1997. Compatible stem taper and stem volume functions for oak (Quercus robur L. and Q. petrae (Matt.) Liebl) in Denmark. Ann For Sci 54(7): 577–595.

Trincado G, Gadow Kv, Sandoval V, 1997. Estimación de volumen comercial en latifoliadas. Bosque 18(1): 39-44.

How to Cite
RodríguezF., LizarraldeI., & BravoF. (2015). Comparison of stem taper equations for eight major tree species in the Spanish Plateau. Forest Systems, 24(3), e034.
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