Equations of bark thickness and volume profiles at different heights with easy-measurement variables

J.M. Cellini, M. Galarza, S.L. Burns, G.J. Martinez-Pastur, M.V. Lencinas


The objective of this work was to develop equations of thickness profile and bark volume at different heights with easy-measurement variables, taking as a study case Nothofagus pumilio forests, growing in different site qualities and growth phases in Southern Patagonia. Data was collected from 717 harvested trees. Three models were fitted using multiple, non-lineal regression and generalized linear model, by stepwise methodology, iteratively reweighted least squares method for maximum likelihood estimation and Marquardt algorithm. The dependent variables were diameter at 1.30 m height (DBH), relative height (RH) and growth phase (GP). The statistic evaluation was made through the adjusted determinant coefficient (r2-adj), standard error of the estimation (SEE), mean absolute error and residual analysis. All models presented good fitness with a significant correlation with the growth phase. A decrease in the thickness was observed when the relative height increase. Moreover, a bark coefficient was made to calculate volume with and without bark of individual trees, where significant differences according to site quality of the stands and DBH class of the trees were observed. It can be concluded that the prediction of bark thickness and bark coefficient is possible using DBH, height, site quality and growth phase, common and easy measurement variables used in forest inventories.


Adler A. 2007. Accumulation of Elements in Salix and Other Species Used in Vegetation Filters with Focus on Wood Fuel Quality. Doctoral Thesis. 34 pp.

Collado L. 2001. Los bosques de la Tierra del Fuego. Análisis de su estratificación mediante imágenes satelitales para el inventario forestal de la provincia. Multiequina 10, 1-16.

Dimitrov ET. 1976. Mathematical models for determining the bark volume of spruce in relation to certain mensurational characteristics. Forest Abstracts 37, 6281.

Esau K. 1969. The phloem. Encyclopedia of Plant Anatomy, Vol. V Part. 2. 505 pp.

Gea G, Martínez Pastur G, Cellini JM, Lencinas MV. 2004. Forty years of silvicultural management in southern Nothofagus pumilio primary forests. Forest Ecology and Management 201: 335-347.

Hamilton F, Chikumbo O. 1997. Modelling upper stem bark thickness for eucalypts. Proceedings for MODSIM 97 Modelling and Simulation Society of Australia Inc., Canberra: International Congress on Modelling and Simulation Vol 4, 1611-1616.

Hastie TJ, Tibshirani RJ. 1986. Generalized additive models. Stat. Sci. 1, 297-318.

Hildebrand-Vogel R, Godoy R, Vogel S. 1990. Subantarctic- Andean Nothofagus pumilio forest. Vegetatio 89: 55-68.

Johnson F. 1966. Bark factors for Douglas-fir. Res. Note PNW-RN-034. U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 4 pp.

Laasasenaho J, Melkas T, Aldén S. 2005. Modelling bark thickness of Picea abies with taper curves. Forest Ecology and Management 206, 35-47.

Marquardt DW. 1963. An algorithm for least squares estimation of nonlinear parameters. Journal of the Society of Industrial and Applied Mathematics 2, 431-441.

Martínez Pastur GJ. 2005. Biometría y Producción Forestal para bosques naturales de Nothofagus pumilio en Tierra del Fuego. Doctoral Thesis. Facultad de Agronomía, Universidad Nacional del Sur. Bahía Blanca. 242 pp.

Martínez Pastur GJ, Fernández MC, Peri P. 1994. Variación de parámetros estructurales y de composición del sotobosque para bosques de Nothofagus pumilio en relación con gradientes ambientales indirectos. Ciencias Forestales 9(1-2), 11-22.

Martínez Pastur GJ, Peri P, Vukasovi? RF, Vaccaro S, Piriz Carrillo V. 1997. Site index equation for Nothofagus pumilio Patagonian forest. Phyton 61, 55-60.

Martínez Pastur GJ, Cellini JM, Peri P, Vukasovi? RF, Fernández MC. 2000, Timber production of Nothofagus pumilio forests by a shelterwood system in Tierra del Fuego (Argentina). Forest Ecology and Management 134, 153-162.

Martínez Pastur GJ, Lencinas MV, Cellini JM, Diaz B, Peri P, Vukasovi? RF. 2002. Herramientas disponibles para la construcción de un modelo de producción para la lenga (Nothofagus pumilio) bajo manejo en un gradiente de calidad de sitio. Bosque 23(2): 69-80.

Martínez Pastur GJ, Lencinas MV, Cellini JM, Peri P, Soler Esteban R. 2009. Timber management with variable retention in Nothofagus pumilio forests of Southern Patagonia. Forest Ecology and Management. 258(4), 436-443.

R Development Core Team. 2011. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria, ISBN 3-900051- 07-0. http://www.R-project.org

Stayton CL, Hoffman M. 1970. Estimating sugar maple bark thickness and volume. Research Paper NC-38. St. Paul, MN: U.S. Dept. of Agriculture, Forest Service, North Central Forest Experiment Station. 12 pp.

Sajdak RL. 1968: Variation in bark characters and wood specific gravity of sugar maple. Eighth Lake States Forest Tree Improvement Conference; Res. Pap. NC-23. St. Paul, MN: U.S. Forest Service, North Central Forest Experiment Station. 10-14.

Schmidt H, Urzúa A. 1982. Transformación y Manejo de los Bosques de lenga en Magallanes. Ciencias Agrícolas 11. 62 pp.

Sonmeza T, Kelesb S, Tilkia F. 2007. Effect of aspect, tree age and tree diameter on bark thickness of Picea orientalis. Scandinavian Journal of Forest Research 22 (3), 193-197.

Trockenbrodt M. 1991. Qualitative structural changes during bark development in Quercus robur, Ulmus glabra, Populus tremula and Betula pendula. IAWA Bull. 12(1), 3-5.

DOI: 10.5424/fs/2112211-01963

Webpage: www.inia.es/Forestsystems