Comparison of methods for estimating heights from complete stem analysis data for Pinus taeda.

Sebastião do Amaral Machado, Luis César Rodrigues da Silva, Marco Aurélio Figura, Saulo Jorge Téo, Rodrigo Geroni Mendes Nascimento


The objective of this research was to compare actual heights at known ages with those estimated by the methods proposed by Graves (1906), Carmean (1972), Lenhart (1972), Newberry (1978), and the Ratio and Graphic methods, in order to identify the most accurate one for Pinus taeda from Southern Brazil. That way, six trees aged at least 11 years were used. Cross-sections with 5 cm thickness were collected at heights of 0.10 meters, 0.70 meters, 1.30 meters and so on at every 1 meter along the bole. True height growth for a given age was measured on the section itself by dividing it in two parts along the pith and looking for the exact point where the true annual height growth took place. The accuracy analyses were based on residuals between true heights and those estimated by the tested methods for each age. For this analysis, the relative mean deviation (D%), relative mean absolute deviation (AbsD%), standard deviation of differences (Sd) and sum of squared relative residuals (SSRR) were calculated. These 4 statistics evaluated together, allowed for the identification of the most accurate method for every age. Complementarily, the non paired t0.05 test for data was applied to evaluate whether the residuals from each method were significant or not. The results of the analysis indicated that Carmean (1972) and Lenhart (1972) were identical owing to the fact that they estimated the same height value for sections where there was only one growth ring finishing in the same section. This situation occurred for most of the results in this current study. It was concluded that Carmean (1972) and Lenhart (1972) were the best methods for estimating height growth because both produced non-significant residuals for the majority of the trees studied.


growth ring; actual heights; cross-section

Texto completo:



CARMEAN, W. H. Site index curves for upland oaks in the central states. Forest Science, Bethesda, v. 18, n. 2, p. 109-120, June/Aug. 1972.

DYER, M. E.; BAILEY, R. L. A Test of six methods for estimating true heights from stem analysis data. Forest Science, Bethesda, v. 33, n.1, p. 3-13, Mar./May 1987.

FABBIO, G.; FRATTEGIANI, M; MANETTI, M. C. Height estimation in stem analysis using second differences. Forest Science, Bethesda, v. 40, n. 2, p. 329-340, May/July 1994.

FIGUEIREDO FILHO, A.; BORDERS, B. E.; HITCH, K. L. Taper equations for Pinus taeda plantations in southern brazil. Forest Ecology and Management, Amsterdam, v. 83, n. 1, p. 39-46, June 1996.

FIGUEIREDO FILHO, A.; SCHAFF, L. B. Comparison between predicted volumes estimated by taper equations and true volumes obtained by the water displacement technique (xylometer). Canadian Journal of Forest Research, Ottawa, v. 29, n. 4, p .451-461, Apr. 1999.

GRAVES, H. S. Forest mensuration. New York: John Wiley & Sons Inc., 1906, 458 p.

KARIUKI, M. Height estimation in complete stem analysis using annual radial growth measurements. Journal of Forestry, Oxford, v. 75, n. 1, p. 63-67, Jan. 2002.

LAPPI, J. Smooth height/age curves from stem analysis with linear programming. Silva Fennica, Helsinki, n. 40, v. 2, p. 291–301, 2006.

LENHART, D. J. An Alternative procedure for improving height/age data from stem analysis. Forest Science, Bethesda, v.18, n. 4, p. 332-332, Dec./Jan. 1972.

NEWBERRY, J. D. A note on Carmean's estimate of height from stem analysis data. Forest Science, Bethesda, v. 37, n.1, p. 368-369, Mar./May 1991.

NEWBERRY, J. D. Dominant height growth models and site index curves for site-prepared slash pine plantations in the lower coastal plain of Georgia and north Florida. Athens: University of Georgia, 1978. 24 f. M. S. Thesis, University of Georgia, Atlanta.

ROSOT, M. A. D. et al. Análise de tronco digital: uma nova metodologia para a medição de anéis de crescimento. Floresta, Curitiba, v. 33, n. 3, p. 235-255, 2003.

SPATHELF, P.; NUTTO, L. Modelagem aplicada ao crescimento e produção florestal. Santa Maria: UFSM/Departamento de Ciências Florestais, 2000. 71 p.


Licença Creative Commons