Variable-top stem biomass equations at tree-level generated by a simultaneous density-integral system for second growth forests of roble, raulí, and coigüe in Chile

Abstract

Variable-top stem biomass models at the tree level for second growth forests of roble (Nothofagus obliqua), raulí (Nothofagus alpina), and coigüe (Nothofagus dombeyi) were fitted by a simultaneous density-integral system, which combines a stem taper model and a wood basic density model. For each model, an autoregressive structure of order 2 and a power equation of residual variance were incorporated to reduce residual autocorrelation and heteroscedasticity, respectively. By using dummy variables in the regression analysis, zonal effects on the parameters in the variable-top stem biomass equations were detected in roble. Consequently, equations for clusters of zones were obtained. These equations presented significant parameters and a high precision in both fitting and validation processes (i.e., CV < 11.5% and CVp < 11.9%, respectively), demonstrating that they are unbiased. The advantage of these types of functions is that they provide estimates of volume and biomass of sections of the stem, defined between any two points of the stem in the three species. Thus, depending on the final use of the wood and the dimensions of the tree, a stem fraction can be quantified in units of volume and the remaining fraction in units of weight.

Keywords

Autocorrelation / Density-integral / Dummy variables / Autoregressive error structure / Heteroscedasticity

References

[1] Akaike H. A new look at the statistical identification model. IEEE Trans Autom Control, 1974, 19(2): 716-723.

[2] Arias-Rodil M, Diéguez-Aranda U, Rodríguez F, López-Sánchez C, Canga E, Cámara A, Castedo-Dorado F. Modelling and localizing a stem taper function for Pinus radiata in Spain. Can J For Res, 2015, 45: 647-658.

[3] Barrio M, Álvarez-González JG, Díaz-Maroto IJ. Elaboración de una tarifa con clasificación de productos para Quercus robur L. en Galicia basada en un modelo de volumen porcentual. Investig Agraria Sist Recur For, 2004, 13: 506-517.

[4] Brooks JR, Lichun J, Alexander C. Compatible stem taper, volume, and weight equations for young longleaf pine plantations in Southwest Georgia. South J Appl For, 2007, 31(4): 187-191.

[5] Brooks JR, Jiang LC, Zhang YJ. Predicting green and dry mass of yellow-poplar: an integral approach. Can J For Res, 2007, 37(4): 786-794.

[6] Brown S, Gillespie A, Lugo A. Biomass estimation methods for tropical forests with applications to forest inventory data. For Sci, 1989, 35(4): 881-902.

[7] Bruce R, Curtis L, Van Coevering C. Development of a system of taper and volume tables for red alder. For Sci, 1968, 14: 339-350.

[8] Calegario N, Gregoire TG, da Silva TA, Filho MT, Alves JA. Integrated system of equations for estimating stem volume, density, and biomass for Australian redcedar (Toona ciliata) plantations. Can J For Res, 2017, 47: 681-689.

[9] Canales AV (2009) Efecto de la intensidad de raleo en el área foliar y la distribución de biomasa en árboles individuales pertenecientes a un renoval puro de roble (Nothofagus oblicua. Mirb. Oerst) de 34 años de edad. Tesis Ingeniero Forestal. Universidad de Concepción, Facultad de Ciencias Forestales, Concepción, Chile, p 29

[10] CONAF (2011) Corporación Nacional Forestal, CL. Catastro de los recursos vegetacionales nativos de Chile. Sección Monitoreo de Ecosistemas Forestales. Santiago, Chile, p 28

[11] Crecente-Campo F, Rojo A, Diéguez-Aranda U. A merchantable volume system for Pinus sylvestris L. in the major mountains ranges of Spain. Ann For Sci, 2009, 66(808): 1-12.

[12] Díaz G, Monteoliva S, Álvarez J, Fernández E. Populus deltoides ‘Australiano 129/60’: variación axial de la densidad y desarrollo de un modelo predictivo de la densidad del árbol completo. Bosque, 2010, 31(1): 65-72.

[13] Diggle PJ, Heagerty P, Liang KY, Zeger SL. Analysis of longitudinal data, 2001 2 Oxford: Oxford University Press.

[14] Donoso P, Donoso C, Sandoval V. Proposición de zonas de crecimiento de renovales de roble (Nothofagus obliqua) y raulí (Nothofagus alpina) en su rango de distribución natural. Bosque, 1993, 14(2): 37-55.

[15] Fang SZ, Yang WZ. Interclonal and within-tree variation in wood properties of poplar clones. J For Res, 2003, 14(4): 263-268.

[16] Fehrmann L, Kleinn C. General considerations about the use of allometric equations for biomass estimation on the example of Norway spruce in central Europe. For Ecol Manag, 2006, 236: 412-421.

[17] Flórez V, Valenzuela C, Acuña E, Cancino J. Combining taper and basic wood density equations for estimating stem biomass of the Populus x canadensis I-488 variety. Bosque, 2014, 35(1): 89-100.

[18] Fonseca W, Alice FG, Rey JM. Modelos para estimar la biomasa de especies nativas en plantaciones y bosques secundarios en la zona Caribe de Costa Rica. Bosque, 2009, 30(1): 36-47.

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

[20] Gayoso J. Medición de la capacidad de captura de carbono en bosques nativos y plantaciones de Chile. Rev For Iberoam, 2002, 1(1): 1-13.

[21] Gayoso J (2013) Funciones alométricas para la determinación de existencias de carbono forestal para la especie Nothofagus obliqua (Mirb.) Oerst. (roble), Santiago, Chile, CONAF, p 41

[22] Gómez-García E, Crecente-Campo F, Diéguez-Aranda U. Selection of mixed-effects parameters in a variable-exponent taper equation for birch trees in northwestern Spain. Ann For Sci, 2013, 70(7): 707-715.

[23] Gregoire TG, Schabenberger O. A non-linear mixed-effects model to predict cumulative bole volume of standing trees. J Appl Stat, 1996, 23(2–3): 257-271.

[24] Gregoire TG, Schabenberger O, Barrett JP. Linear modeling of irregularly spaced, unbalanced, longitudinal data from permanent plot measurement. Can J For Res, 1995, 25: 137-156.

[25] Hardy M (1993) Regression with dummy variables. Sage university paper series on quantitative applications in the Social Sciences, 07–093. Sage, Newbury Park, CA

[26] Harvey AC. Estimating regression models with multiplicative heteroscedasticity. Econometrica, 1976, 44(3): 461-465.

[27] Jordan L, Souter R, Parresol B, Daniels RF. Application of the algebraic difference approach for developing self-referencing specific gravity and biomass equations. For Sci, 2006, 52(1): 81-92.

[28] Kozak A. Effects of multicollinearity and autocorrelation on the variable-exponent taper functions. Can J For Res, 1997, 27(5): 619-629.

[29] Lara A, Donoso C, Donoso P, Nuñez P, Cavieres A (1999) Normas de manejo para raleo de renovales del tipo forestal roble–raulí–coigüe. In: Silvicultura de los bosques nativos de Chile. 1a Ed. Universitaria, Santiago, Chile, pp 129–144

[30] Leites LP, Robinson AP. Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework. For Sci, 2004, 50: 204-212.

[31] Li CP, Xiao CW. Above- and belowground biomass of Artemisia ordosica communities in three contrasting habitats of the Mu Us desert, northern China. J Arid Environ, 2007, 70: 195-207.

[32] Lindstrom MJ, Bates DM. Nonlinear mixed effects models for repeated measures data. Biometrics, 1990, 46: 673-687.

[33] Muñoz L (2013) Desarrollo de modelos flexibles para la determinación de biomasa fustal de Pinus radiata D. Don en suelos trumaos de la Precordillera andina. Tesis Ingeniero Forestal. Universidad de Concepción, Facultad de Ciencias Forestales, Concepción, Chile, p 32

[34] Návar CJ, Gonzáles N, Graciano J (2001) Ecuaciones para estimar el rendimiento e incremento de biomasa total en plantaciones forestales de Durango, México. Simposio internacional medición y monitoreo de la captura de carbono en ecosistemas forestales, Valdivia-Chile, p 13

[35] Návar J, Nájera J, Jurado E. Biomass estimation equations in the Tamaulipan thornscrub of northeastern Mexico. J Arid Environ, 2002, 52: 167-179.

[36] Neter J, Kutner MH, Nachtsheim CJ, Wasserman W. Applied linear statistical models, 1998, New York: Mc Graw-Hill 1408

[37] ODEPA (2000) Oficinas De Estudios y Políticas Agrarias. Clasificación de las explotaciones agrícolas del VI censo nacional agropecuario según tipo de productor y localización geográfica. Ministerio de Agricultura. Documento de trabajo No. 5. I.S.S.N. 0717−0378. Santiago, Chile, p 91

[38] Ott P (1997) The use of indicator variables in non-linear regression. Biometrics information. Ministry of Forests Research Program, British Columbia. Pamphlet 56

[39] Parresol BR, Thomas CE. A density integral approach to estimating stem biomass. For Ecol Manag, 1989, 26: 285-297.

[40] Parresol BR, Thomas CE. A simultaneous density-integral system for estimating stem profile and biomass: slash pine and willow oak. Can J For Res, 1996, 26: 773-781.

[41] Prodan M, Peters R, Cox F, Real P. Mensura forestal, 1997, San José: IICA-GTZ 561

[42] Sáez M (1991) Biomasa y contenido de nutrientes de renovales no intervenidos roble–raulí (Nothofagus obliqua (Mirb) Oerst—Nothofagus alpina (Poepp. et Endl.) Oerst) en suelos volcánicos de la Precordillera Andina, IX Región, Tesis de Grado. Universidad de Chile, Escuela de Ciencias Forestales, Santiago, Chile, p 96

[43] SAS. SAS/STAT^® 9.2 user’s guide, 2009 2 Cary, NC: SAS Institute Inc..

[44] Tasissa G, Burkhart HE. An application of mixed effects analysis to modeling thinning effects on stem profile of loblolly pine. For Ecol Manag, 1998, 103: 87-101.

[45] Teshome T. A ratio method for predicting stem merchantable volume and associated taper equations for Cupressus lusitanica, Ethiopia. For Ecol Manag, 2005, 204: 171-179.

[46] Thomas CE, Parresol BR, Lê KH, Lohrey RE. Biomass and taper for trees in thinned and unthinned longleaf pine plantations. South J Appl For, 1995, 19(1): 29-35.

[47] Trincado G, Burkhart HE. A generalized approach for modeling and localizing stem profiles curves. For Sci, 2006, 52: 670-682.

[48] Vargas-Larreta B, López-Sanchez CA, Corral-Rivas JJ, López-Martínez JO, Aguirre-Calderon CG, Álvarez-González JG. Allometric equations for estimating biomass and carbon stocks in the temperate forests of North-Western Mexico. Forests, 2017, 8: 269.

[49] Ver Planck NR, Macfarlane DW. A vertically integrated whole-tree biomass model. Trees, 2015, 29: 449-460.

[50] Yang YQ, Huang SM, Meng SX. Development of a tree-specific stem profile model for white spruce: a nonlinear mixed model approach with a generalized covariance structure. Forestry, 2009, 82(5): 541-555.

[51] Zakrzewski WT, Duchesne I. Stem biomass model for jack pine (Pinus banksiana Lamb.) in Ontario. For Ecol Manag, 2012, 279: 112-120.

[52] Zhang YJ, Borders BE, Bailey RL. Derivation, fitting, and implication of a compatible stem taper-volume-weight system for intensively managed, fast growing loblolly pine. For Sci, 2002, 48(3): 595-607.

[53] Zimmerman D, Núñez-Antón V. Parametric modelling of growth curve data: an overview. Test, 2001, 10(1): 1-73.