Floresta e Ambiente
Floresta e Ambiente
Original Article Forest Management

Allometric models to biomass in restoration areas in the Atlantic rain forest

Emanuel José Gomes de Araújo; Gabrielle Hambrecht Loureiro; Carlos Roberto Sanquetta; Mateus Niroh Inoue Sanquetta; Ana Paula Dalla Corte; Sylvio Péllico Netto; Alexandre Behling


ABSTRACT: The objective of the study was to present mathematical models and strategies for fitting equations to estimate dry biomass for tree species in forest restoration areas. The presence of outliers was analyzed in each fitted equation using values of the matrix H, leverage points, means of standard and studentized residuals, and of influential points through DFFITS, DFBETAS and COOK distance values. Furthermore, the normality, homoscedasticity and independence of residuals were checked. The accuracy of the fitted equations was evaluated by means of the R2adj., Syx, analysis of residuals, and AIC and BIC criteria. The results showed that the model for estimating dry biomass as a function of the variables Dc2, DBH2, Hc2 and DBH provides the more accurate solution, with Syx = 40.91% and R2adj. = 0.92. We concluded that the performance of this equation improves when adjusted to data stratified by classes of height-diameter ratio, which reduces the value of the estimated error.


modeling, dry weight, carbon, allometry


Addo-Fordjour P, Rahmad ZB. Development of allometric equations for estimating above-ground liana biomass in tropical primary and secondary forests, Malaysia. International Journal of Ecology 2013; 2013: 1-9.

Akaike H. Information Theory and an Extension of the Maximum Likelihood Principle. In: Parzen E, Tanabe K, Kitagawa G, editors. Selected Papers of Hirotugu Akaike. New York: Springer; 1998. (Perspectives in Statistics).

Barbosa ERM, Langevelde F, Tomlinson KW, Carvalheiro LG, Kirkman K, Bie S et al. Tree species from different functional groups respond differently to environmental changes during establishment. Oecologia 2014; 174(4): 1345-1357. PMid:24337711. http://dx.doi.org/10.1007/s00442-013-2853-y.

Baskerville GL. Use of logarithmic regression in the estimation of plant biomass. Canadian Journal of Forest Research 1972; 2(1): 49-53. http://dx.doi.org/10.1139/x72-009.

Brasil. Ministério da Agricultura e Reforma Agrária. Normais climatológicas 1961-1990. Brasília: Mara; 1992.

Chave J, Andalo C, Brown S, Cairns MA, Chambers JQ, Eamus D et al. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia 2005; 145(1): 87-99. PMid:15971085. http://dx.doi.org/10.1007/s00442-005-0100-x.

Chen JM, Liu J, Leblanc SG, Lacaze R, Roujean J-L. Multi-angular optical remote sensing for assessing vegetation structure and carbon absorption. Remote Sensing of Environment 2003; 84(4): 516-525. http://dx.doi.org/10.1016/S0034-4257(02)00150-5.

Corte APD, Sanquetta CR. Quantificação do estoque de carbono fixado em reflorestamento de Pinus na área de domínio de da floresta Ombrófila Mista no Paraná. Cerne 2007; 13(1): 32-39.

Cunha US, Machado AS, Figueiredo Filho A. Uso de análise exploratória de dados e de regressão robusta na avaliação do crescimento de espécies comerciais de terra firme da Amazônia. Árvore 2002; 26(4): 391-402.

Drolet GG, Huemmrich KF, Hall FG, Middleton EM, Black TA, Barr AG et al. A Modis-derived photochemical reflectance index to detect inter-annual variations in the photosynthetic light-use efficiency of a boreal deciduous forest. Remote Sensing of Environment 2005; 98(2-3): 212-224. http://dx.doi.org/10.1016/j.rse.2005.07.006.

Frankenberg C, Fisher JB, Worden J. New global observations of the terrestrial carbon cycle from GOSAT: Patterns of plant fluorescence with gross primary productivity. Geophysical Research Letters 2011; 38(17): L17706.

Gehring C, Park S, Denich M. Liana allometric biomass equations for Amazonian primary and secondary forest. Forest Ecology and Management 2004; 195(1-2): 69-83. http://dx.doi.org/10.1016/j.foreco.2004.02.054.

Goetz SJ, Prince SD, Goward SN, Thawley MM, Small J. Satellite remote sensing of primary production: An improved production efficiency modeling approach. Ecological Modelling 1999; 122(3): 239-255. http://dx.doi.org/10.1016/S0304-3800(99)00140-4.

Higuchi N, Santos J, Ribeiro RJ, Minette L, Biot Y. Biomassa da parte aérea da vegetação da floresta tropical úmida de terra-firme da Amazônia brasileira. Acta Amazonica 1998; 28(2): 153-166. http://dx.doi.org/10.1590/1809-43921998282166.

Kenzo T, Ichie T, Hattori D, Itioka T, Handa C, Ohkubo T et al. Development of allometric relationships for accurate estimation of above- and below-ground biomass in tropical secondary forests in Sarawak, Malaysia. Journal of Tropical Ecology 2009; 25(04): 371-386. http://dx.doi.org/10.1017/S0266467409006129.

Ketterings QM, Coe R, Noordwijk M, Ambagau Y, Palm CA. Reducing uncertainty in the use of allometric biomass equations for predicting above-ground tree biomass in mixed secondary forests. Forest Ecology and Management 2001; 146(1-3): 199-209. http://dx.doi.org/10.1016/S0378-1127(00)00460-6.

Kramer PJ, Koslowski T. Fisiologia das árvores. Lisboa: Fundação Calouste Gulbenkian; 1972.

Larcher W. Ecofisiologia vegetal. São Paulo: EPU; 1986.

Litton CM, Kauffman JB. Allometric models for predicting aboveground biomass in two widespread woody plants in Hawaii. Biotropica 2008; 40(3): 313-320. http://dx.doi.org/10.1111/j.1744-7429.2007.00383.x.

Luo Y, Zhang X, Wang X, Ren Y. Dissecting variation in biomass conversion factors across China’s Forests: implications for biomass and carbon accounting. PLoS One 2014; 9(4): e94777. PMid:24728222. http://dx.doi.org/10.1371/journal.pone.0094777.

Melo LC, Sanquetta CR, Corte APD, Hentz AK. Estimativa de biomassa e carbono total para árvores de caixeta no Paraná. Pesquisa Florestal Brasileira 2014; 77(77): 21-29. http://dx.doi.org/10.4336/2014.pfb.34.77.592.

Moore JR. Allometric equations to predict the total above-ground biomass of radiata pine trees. Annals of Forest Science 2010; 67(8): 1-11. http://dx.doi.org/10.1051/forest/2010042.

Morais VA, Scolforo JRS, Silva CA, Mello JM, Gomide LR, Oliveira AD. Carbon and biomass stocks in a fragment of cerradão in Minas Gerais state, Brazil. Cerne 2013a; 19(2): 237-245. http://dx.doi.org/10.1590/S0104-77602013000200007.

Morais VA, Silva CA, Scolforo JRS, Mello JM, Araújo EJG, Assis EA. Modelagem do teor de carbono orgânico em solos de fragmentos de cerrado de Januária e Bonito de Minas, Minas Gerais. Pesquisa Florestal Brasileira 2013b; 76(76): 343-354. http://dx.doi.org/10.4336/2013.pfb.33.76.507.

Nogueira EM, Fearnside PM, Nelson BW. Normalization of wood density in biomass estimates of Amazon forests. Forest Ecology and Management 2008; 256(5): 990-996. http://dx.doi.org/10.1016/j.foreco.2008.06.001.

Péllico Netto S, Brena DA. Inventário florestal. Curitiba: UFPR, UFSM; 1997.

R Development Core Team. R: a language and environment for statistical computing [online]. Vienna: R Foundation for Statistical Computing; 2001. [cited 2017 Nov 10]. Available from: www.R-project.org

Regazzi AJ. Teste para verificar a identidade de modelos de regressão e a igualdade de alguns parâmetros num modelo polinomial ortogonal. Revista Ceres 1992; 228: 176-195.

Rezende AV, Vale AT, Sanquetta CR, Figueiredo A Fo, Felfili JM. Comparação de modelos matemáticos para estimativa do volume, biomassa e estoque de carbono da vegetação lenhosa de um cerrado sensu stricto em Brasília, DF. Scientia Forestalis 2006; 71: 65-76.

Rochadelli R. Estrutura de fixação dos átomos de carbono em reflorestamento (Estudo de caso: Mimosa scabrella Bentham, Bracatinga) [Tese]. Curitiba: Setor de Ciências Agrárias, Universidade Federal do Paraná; 2001.

Sanquetta CR, Balbinot R, Ziliotto MAB. Fixação de carbono: atualidades, projetos e pesquisas. Curitiba: AM Impressos; 2004.

Schwarz G. Estimating the dimensional of a model. Annals of Statistics 1978; 6(2): 461-464. http://dx.doi.org/10.1214/aos/1176344136.

Scolforo JR, Rufini AL, Mello JM, Trugilho PF, Oliveira AD, Silva CPC. Equações para peso de matéria seca das fisionomias, em Minas Gerais. In: Scolforo JRS, Oliveira AD, Acerbi FW Jr. Inventário florestal de Minas Gerais: equações de volume, peso de matéria seca e carbono para diferentes fitofisionomias da flora nativa. Lavras: UFLA; 2008.

Scolforo JRS. Biometria florestal: parte I - modelos de regressão linear e não linear; parte II - modelos para relação hipsométrica, volume, afilamento e peso de matéria seca. Lavras: UFLA, FAEPE; 2005. 352 p.

Segura M, Kanninen M. Allometric models for tree volume and total aboveground biomass in a tropical humid forest in Costa Rica. Biotropica 2005; 37(1): 2-8. http://dx.doi.org/10.1111/j.1744-7429.2005.02027.x.

Soares BS Fo, Nepstad DC, Curran LM, Cerqueira GC, Garcia RA, Ramos CA et al. Modeling conservation in the Amazon basin. Nature 2006; 440(7083): 520-523. PMid:16554817. http://dx.doi.org/10.1038/nature04389.

Song C, Dannenberg MP, Hwang T Optical remote sensing of terrestrial ecosystem primary productivity. Progress in Physical Geography 2013; 37(6): 834-854. http://dx.doi.org/10.1177/0309133313507944.

Urbano E, Machado AS, Figueiredo-Filho A, Koehler HS. Equações para estimar o peso de carbono fixado em árvores de Mimosa scabrella Bentham (bracatinga) em povoamentos nativos. Cerne 2008; 14(3): 194-203.

Vogel HLM, Schumacher MV, Trüby P. Quantificação da biomassa em uma Floresta Estacional Decidual em Itaara, RS, Brasil. Ciência Florestal 2006; 16(4): 419-425. http://dx.doi.org/10.5902/198050981923.

Wang C. Biomass allometric equations for 10 co-occurring tree species in Chinese temperate forests. Forest Ecology and Management 2006; 222(1-3): 9-16. http://dx.doi.org/10.1016/j.foreco.2005.10.074.

Watzlawick LF, Kirchner FF, Sanquetta CR. Estimativa de biomassa e carbono em floresta com Araucaria utilizando Imagens do satélite ikonos II. Ciência Florestal 2009; 19(2): 169-181. http://dx.doi.org/10.5902/19805098408.

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