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
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摘要
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.
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.
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.
引文
Akaike H(1974)A new look at the statistical identification model.IEEE Trans Autom Control 19(2):716-723
Arias-Rodil M,Diéguez-Aranda U,Rodríguez F,López-Sánchez C,Canga E,Cámara A,Castedo-Dorado F(2015)Modelling and localizing a stem taper function for Pinus radiata in Spain.Can JFor Res 45:647-658
Barrio M,Alvarez-González JG,Díaz-Maroto IJ(2004)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 13:506-517
Brooks JR,Lichun J,Alexander C(2007a)Compatible stem taper,volume,and weight equations for young longleaf pine plantations in Southwest Georgia.South J Appl For 31(4):187-191
Brooks JR,Jiang LC,Zhang YJ(2007b)Predicting green and dry mass of yellow-poplar:an integral approach.Can J For Res37(4):786-794
Brown S,Gillespie A,Lugo A(1989)Biomass estimation methods for tropical forests with applications to forest inventory data.For Sci 35(4):881-902
Bruce R,Curtis L,Van Coevering C(1968)Development of a system of taper and volume tables for red alder.For Sci 14:339-350
Calegario N,Gregoire TG,da Silva TA,Filho MT,Alves JA(2017)Integrated system of equations for estimating stem volume,density,and biomass for Australian redcedar(Toona ciliata)plantations.Can J For Res 47:681-689
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)de34 a?os de edad.Tesis Ingeniero Forestal.Universidad de Concepción,Facultad de Ciencias Forestales,Concepción,Chile,p 29
CONAF(2011)Corporación Nacional Forestal,CL.Catastro de los recursos vegetacionales nativos de Chile.Sección Monitoreo de Ecosistemas Forestales.Santiago,Chile,p 28
Crecente-Campo F,Rojo A,Diéguez-Aranda U(2009)A merchantable volume system for Pinus sylvestris L.in the major mountains ranges of Spain.Ann For Sci 66(808):1-12
Díaz G,Monteoliva S,Alvarez J,Fernández E(2010)Populus deltoides‘Australiano 129/60’:variación axial de la densidad y desarrollo de un modelo predictivo de la densidad del árbol completo.Bosque 31(1):65-72
Diggle PJ,Heagerty P,Liang KY,Zeger SL(2001)Analysis of longitudinal data,2nd edn.Oxford University Press,Oxford
Donoso P,Donoso C,Sandoval V(1993)Proposición de zonas de crecimiento de renovales de roble(Nothofagus obliqua)y raulí(Nothofagus alpina)en su rango de distribución natural.Bosque14(2):37-55
Fang SZ,Yang WZ(2003)Interclonal and within-tree variation in wood properties of poplar clones.J For Res 14(4):263-268
Fehrmann L,Kleinn C(2006)General considerations about the use of allometric equations for biomass estimation on the example of Norway spruce in central Europe.For Ecol Manag 236:412-421
Flórez V,Valenzuela C,Acu?a E,Cancino J(2014)Combining taper and basic wood density equations for estimating stem biomass of the Populus x canadensis I-488 variety.Bosque 35(1):89-100
Fonseca W,Alice FG,Rey JM(2009)Modelos para estimar la biomasa de especies nativas en plantaciones y bosques secundarios en la zona Caribe de Costa Rica.Bosque 30(1):36-47
Garber SM,Maguire DA(2003)Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures.For Ecol Manag 179:507-522
Gayoso J(2002)Medición de la capacidad de captura de carbono en bosques nativos y plantaciones de Chile.Rev For Iberoam1(1):1-13
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
Gómez-García E,Crecente-Campo F,Diéguez-Aranda U(2013)Selection of mixed-effects parameters in a variable-exponent taper equation for birch trees in northwestern Spain.Ann For Sci70(7):707-715
Gregoire TG,Schabenberger O(1996)A non-linear mixed-effects model to predict cumulative bole volume of standing trees.J Appl Stat 23(2-3):257-271
Gregoire TG,Schabenberger O,Barrett JP(1995)Linear modeling of irregularly spaced,unbalanced,longitudinal data from permanent plot measurement.Can J For Res 25:137-156
Hardy M(1993)Regression with dummy variables.Sage university paper series on quantitative applications in the Social Sciences,07-093.Sage,Newbury Park,CA
Harvey AC(1976)Estimating regression models with multiplicative heteroscedasticity.Econometrica 44(3):461-465
Jordan L,Souter R,Parresol B,Daniels RF(2006)Application of the algebraic difference approach for developing self-referencing specific gravity and biomass equations.For Sci 52(1):81-92
Kozak A(1997)Effects of multicollinearity and autocorrelation on the variable-exponent taper functions.Can J For Res27(5):619-629
Lara A,Donoso C,Donoso P,Nu?ez 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
Leites LP,Robinson AP(2004)Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework.For Sci 50:204-212
Li CP,Xiao CW(2007)Above-and belowground biomass of Artemisia ordosica communities in three contrasting habitats of the Mu Us desert,northern China.J Arid Environ 70:195-207
Lindstrom MJ,Bates DM(1990)Nonlinear mixed effects models for repeated measures data.Biometrics 46:673-687
Mu?oz 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
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
Návar J,Nájera J,Jurado E(2002)Biomass estimation equations in the Tamaulipan thornscrub of northeastern Mexico.J Arid Environ 52:167-179
Neter J,Kutner MH,Nachtsheim CJ,Wasserman W(1998)Applied linear statistical models.Mc Graw-Hill,New York,p 1408
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
Ott P(1997)The use of indicator variables in non-linear regression.Biometrics information.Ministry of Forests Research Program,British Columbia.Pamphlet 56
Parresol BR,Thomas CE(1989)A density integral approach to estimating stem biomass.For Ecol Manag 26:285-297
Parresol BR,Thomas CE(1996)A simultaneous density-integral system for estimating stem profile and biomass:slash pine and willow oak.Can J For Res 26:773-781
Prodan M,Peters R,Cox F,Real P(1997)Mensura forestal.IICA-GTZ,San José,p 561
Sáez M(1991)Biomasa y contenido de nutrientes de renovales no intervenidos roble-raulí(Nothofagus obliqua(Mirb)OerstNothofagus 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
SAS(2009)SAS/STATò9.2 user’s guide,2nd edn.SAS Institute Inc.,Cary,NC
Tasissa G,Burkhart HE(1998)An application of mixed effects analysis to modeling thinning effects on stem profile of loblolly pine.For Ecol Manag 103:87-101
Teshome T(2005)A ratio method for predicting stem merchantable volume and associated taper equations for Cupressus lusitanica,Ethiopia.For Ecol Manag 204:171-179
Thomas CE,Parresol BR,LêKH,Lohrey RE(1995)Biomass and taper for trees in thinned and unthinned longleaf pine plantations.South J Appl For 19(1):29-35
Trincado G,Burkhart HE(2006)A generalized approach for modeling and localizing stem profiles curves.For Sci52:670-682
Vargas-Larreta B,López-Sanchez CA,Corral-Rivas JJ,LópezMartínez JO,Aguirre-Calderon CG,Alvarez-González JG(2017)Allometric equations for estimating biomass and carbon stocks in the temperate forests of North-Western Mexico.Forests8:269
Ver Planck NR,Macfarlane DW(2015)A vertically integrated whole-tree biomass model.Trees 29:449-460
Yang YQ,Huang SM,Meng SX(2009)Development of a treespecific stem profile model for white spruce:a nonlinear mixed model approach with a generalized covariance structure.Forestry 82(5):541-555
Zakrzewski WT,Duchesne I(2012)Stem biomass model for jack pine(Pinus banksiana Lamb.)in Ontario.For Ecol Manag279:112-120
Zhang YJ,Borders BE,Bailey RL(2002)Derivation,fitting,and implication of a compatible stem taper-volume-weight system for intensively managed,fast growing loblolly pine.For Sci48(3):595-607
Zimmerman D,Nú?ez-Antón V(2001)Parametric modelling of growth curve data:an overview.Test 10(1):1-73
Arias-Rodil M,Diéguez-Aranda U,Rodríguez F,López-Sánchez C,Canga E,Cámara A,Castedo-Dorado F(2015)Modelling and localizing a stem taper function for Pinus radiata in Spain.Can JFor Res 45:647-658
Barrio M,Alvarez-González JG,Díaz-Maroto IJ(2004)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 13:506-517
Brooks JR,Lichun J,Alexander C(2007a)Compatible stem taper,volume,and weight equations for young longleaf pine plantations in Southwest Georgia.South J Appl For 31(4):187-191
Brooks JR,Jiang LC,Zhang YJ(2007b)Predicting green and dry mass of yellow-poplar:an integral approach.Can J For Res37(4):786-794
Brown S,Gillespie A,Lugo A(1989)Biomass estimation methods for tropical forests with applications to forest inventory data.For Sci 35(4):881-902
Bruce R,Curtis L,Van Coevering C(1968)Development of a system of taper and volume tables for red alder.For Sci 14:339-350
Calegario N,Gregoire TG,da Silva TA,Filho MT,Alves JA(2017)Integrated system of equations for estimating stem volume,density,and biomass for Australian redcedar(Toona ciliata)plantations.Can J For Res 47:681-689
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)de34 a?os de edad.Tesis Ingeniero Forestal.Universidad de Concepción,Facultad de Ciencias Forestales,Concepción,Chile,p 29
CONAF(2011)Corporación Nacional Forestal,CL.Catastro de los recursos vegetacionales nativos de Chile.Sección Monitoreo de Ecosistemas Forestales.Santiago,Chile,p 28
Crecente-Campo F,Rojo A,Diéguez-Aranda U(2009)A merchantable volume system for Pinus sylvestris L.in the major mountains ranges of Spain.Ann For Sci 66(808):1-12
Díaz G,Monteoliva S,Alvarez J,Fernández E(2010)Populus deltoides‘Australiano 129/60’:variación axial de la densidad y desarrollo de un modelo predictivo de la densidad del árbol completo.Bosque 31(1):65-72
Diggle PJ,Heagerty P,Liang KY,Zeger SL(2001)Analysis of longitudinal data,2nd edn.Oxford University Press,Oxford
Donoso P,Donoso C,Sandoval V(1993)Proposición de zonas de crecimiento de renovales de roble(Nothofagus obliqua)y raulí(Nothofagus alpina)en su rango de distribución natural.Bosque14(2):37-55
Fang SZ,Yang WZ(2003)Interclonal and within-tree variation in wood properties of poplar clones.J For Res 14(4):263-268
Fehrmann L,Kleinn C(2006)General considerations about the use of allometric equations for biomass estimation on the example of Norway spruce in central Europe.For Ecol Manag 236:412-421
Flórez V,Valenzuela C,Acu?a E,Cancino J(2014)Combining taper and basic wood density equations for estimating stem biomass of the Populus x canadensis I-488 variety.Bosque 35(1):89-100
Fonseca W,Alice FG,Rey JM(2009)Modelos para estimar la biomasa de especies nativas en plantaciones y bosques secundarios en la zona Caribe de Costa Rica.Bosque 30(1):36-47
Garber SM,Maguire DA(2003)Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures.For Ecol Manag 179:507-522
Gayoso J(2002)Medición de la capacidad de captura de carbono en bosques nativos y plantaciones de Chile.Rev For Iberoam1(1):1-13
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
Gómez-García E,Crecente-Campo F,Diéguez-Aranda U(2013)Selection of mixed-effects parameters in a variable-exponent taper equation for birch trees in northwestern Spain.Ann For Sci70(7):707-715
Gregoire TG,Schabenberger O(1996)A non-linear mixed-effects model to predict cumulative bole volume of standing trees.J Appl Stat 23(2-3):257-271
Gregoire TG,Schabenberger O,Barrett JP(1995)Linear modeling of irregularly spaced,unbalanced,longitudinal data from permanent plot measurement.Can J For Res 25:137-156
Hardy M(1993)Regression with dummy variables.Sage university paper series on quantitative applications in the Social Sciences,07-093.Sage,Newbury Park,CA
Harvey AC(1976)Estimating regression models with multiplicative heteroscedasticity.Econometrica 44(3):461-465
Jordan L,Souter R,Parresol B,Daniels RF(2006)Application of the algebraic difference approach for developing self-referencing specific gravity and biomass equations.For Sci 52(1):81-92
Kozak A(1997)Effects of multicollinearity and autocorrelation on the variable-exponent taper functions.Can J For Res27(5):619-629
Lara A,Donoso C,Donoso P,Nu?ez 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
Leites LP,Robinson AP(2004)Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework.For Sci 50:204-212
Li CP,Xiao CW(2007)Above-and belowground biomass of Artemisia ordosica communities in three contrasting habitats of the Mu Us desert,northern China.J Arid Environ 70:195-207
Lindstrom MJ,Bates DM(1990)Nonlinear mixed effects models for repeated measures data.Biometrics 46:673-687
Mu?oz 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
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
Návar J,Nájera J,Jurado E(2002)Biomass estimation equations in the Tamaulipan thornscrub of northeastern Mexico.J Arid Environ 52:167-179
Neter J,Kutner MH,Nachtsheim CJ,Wasserman W(1998)Applied linear statistical models.Mc Graw-Hill,New York,p 1408
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
Ott P(1997)The use of indicator variables in non-linear regression.Biometrics information.Ministry of Forests Research Program,British Columbia.Pamphlet 56
Parresol BR,Thomas CE(1989)A density integral approach to estimating stem biomass.For Ecol Manag 26:285-297
Parresol BR,Thomas CE(1996)A simultaneous density-integral system for estimating stem profile and biomass:slash pine and willow oak.Can J For Res 26:773-781
Prodan M,Peters R,Cox F,Real P(1997)Mensura forestal.IICA-GTZ,San José,p 561
Sáez M(1991)Biomasa y contenido de nutrientes de renovales no intervenidos roble-raulí(Nothofagus obliqua(Mirb)OerstNothofagus 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
SAS(2009)SAS/STATò9.2 user’s guide,2nd edn.SAS Institute Inc.,Cary,NC
Tasissa G,Burkhart HE(1998)An application of mixed effects analysis to modeling thinning effects on stem profile of loblolly pine.For Ecol Manag 103:87-101
Teshome T(2005)A ratio method for predicting stem merchantable volume and associated taper equations for Cupressus lusitanica,Ethiopia.For Ecol Manag 204:171-179
Thomas CE,Parresol BR,LêKH,Lohrey RE(1995)Biomass and taper for trees in thinned and unthinned longleaf pine plantations.South J Appl For 19(1):29-35
Trincado G,Burkhart HE(2006)A generalized approach for modeling and localizing stem profiles curves.For Sci52:670-682
Vargas-Larreta B,López-Sanchez CA,Corral-Rivas JJ,LópezMartínez JO,Aguirre-Calderon CG,Alvarez-González JG(2017)Allometric equations for estimating biomass and carbon stocks in the temperate forests of North-Western Mexico.Forests8:269
Ver Planck NR,Macfarlane DW(2015)A vertically integrated whole-tree biomass model.Trees 29:449-460
Yang YQ,Huang SM,Meng SX(2009)Development of a treespecific stem profile model for white spruce:a nonlinear mixed model approach with a generalized covariance structure.Forestry 82(5):541-555
Zakrzewski WT,Duchesne I(2012)Stem biomass model for jack pine(Pinus banksiana Lamb.)in Ontario.For Ecol Manag279:112-120
Zhang YJ,Borders BE,Bailey RL(2002)Derivation,fitting,and implication of a compatible stem taper-volume-weight system for intensively managed,fast growing loblolly pine.For Sci48(3):595-607
Zimmerman D,Nú?ez-Antón V(2001)Parametric modelling of growth curve data:an overview.Test 10(1):1-73