Compatible Tree Volume Equations and Heteroscedasticity for Dahurian Larch in Different Region of Daxing'anling

LIU Jing-ting; JIANG Li-chun

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Compatible Tree Volume Equations and Heteroscedasticity for Dahurian Larch in Different Region of Daxing'anling

LIU Jing-ting¹,
JIANG Li-chun^1,

1.
College of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, China

Received Date: 2015-09-10

Abstract

[Objective] Making a detailed comparative analysis of compatible volume models in different regions and different heteroscedasticity correction methods, developing compatible volume equations to estimate different regions for Dahurian larch (Larix gmelini Rupr.) in Daxing'anling.[Method] Regional differences in volume models were examined and tested using the nonlinear extra sum of squares method (F-test). Weighted regression was used to decrease the heteroscedasticity of volume equations in three regions using variety forms of weight functions.[Result] The results indicated that the volume models were significantly different among different regions (PF(x), 1/D4.99, 1/D3.38 for region 1(-0.11, 0.97), region 2(0.04, 0.08), and region 3(1.04, 0.93) respectively.[Conclusion] Individual tree volume model is a major component of forest inventory and growth and yield model. Prediction errors of compatible volume models were within ±3% in three different regions. Compatible volume models should consider the phenomena of heteroscedasticity, and the optimal weight functions of individual tree volume models don't have a uniform format. To get the stability of parameters estimation, different weight functions should be analyzed in the process of the weighted regression.
- Larix gmelini,
- compatibility,
- regional test,
- heteroscedasticity

References

[1]	Amateis R L, Burkhart H E. Cubic-foot volume equations for loblolly pine trees in cutover, site-prepared plantations[J]. Southern Journal of Applied Forestry, 1987, 11(4):190-192.
[2]	Fowler G W. Individual tree volume equations for red pine in Michigan[J]. Northern Journal of Applied Forestry, 1997, 14(2):53-58.
[3]	曾伟生. 杉木相容性立木材积表系列模型研建[J]. 林业科学研究, 2014, 27(1):6-10.
[4]	张会儒, 唐守正. 与材积兼容的生物量模型的建立及其估计方法研究[J]. 林业科学研究, 1999, 12(1):53-59.
[5]	Snorrason A, Einarsson S F. Single-tree biomass and stem volume functions for eleven tree species used in Icelandic forestry[J]. Icelandic Agricultural Sciences, 2006, 19:15-24.
[6]	Brooks J R, Wiant H V. Ecoregion-based local volume equations for Appalachian hardwoods[J]. Northern Journal of Applied Forestry, 2008, 25(2):87-92.
[7]	Case B S, Hall R J. Assessing prediction errors of generalized tree biomass and volume equations for the boreal forest region of west-central Canada[J]. Canadian Journal of Forest Research, 2008, 38(4):878-889.
[8]	胥辉. 一种与材积相容的生物量模型[J]. 北京林业大学学报, 1999, 21(5):32-36.
[9]	曾鸣, 聂祥永, 曾伟生. 中国杉木相容性立木材积和地上生物量方程[J]. 林业科学, 2013, 49(10):74-79.
[10]	Tang S, Li Y, Wang Y. Simultaneous equations, error-in-variable models, and model integration in systems ecology[J]. Ecological Modelling, 2001, 142(3):285-294.
[11]	Tang S, Wang Y. A parameter estimation program for the error-in-variable model[J]. Ecological Modelling, 2002, 156(2):225-236.
[12]	Fortin M,Daigle C,Ung C, et al. A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling[J]. European Journal of Forest Research, 2007, 126:573-585.
[13]	McRoberts R, Westfall J. Effects of uncertainty in model predictions of individual tree volume on large area volume estimates[J]. Forest Science, 2014, 60(1):34-42
[14]	吴明山, 胥辉, 叶江霞. 兴安落叶松材积模型中的异方差研究[J]. 山东林业科技, 2010, 40(2):14-17.
[15]	Huang S, Price D, Titus S J. Development of ecoregion-based height-diameter models for white spruce in boreal forests[J]. Forest Ecology and Management, 2000, 129(1):125-141.
[16]	Peng C, Zhang L, Liu J. Developing and validating nonlinear height-diameter models for major Tree species of Ontario's boreal forests[J]. Northern Journal of Applied Forestry, 2001, 18(3):87-94.
[17]	夏忠胜, 曾伟生, 朱松, 等. 贵州省人工杉木立木材积方程研建[J]. 北京林业大学学报, 2012, 34(1):1-5.
[18]	Zhang L, Peng C, Huang S, et al. Development and evaluation of ecoregion-based jack pine height-diameter models for Ontario[J]. The Forestry Chronicle, 2002, 78(4):530-538.
[19]	Peng C, Zhang L, Zhou X, et al. Developing and evaluating tree height-diameter models at three geographic scales for black spruce in Ontario[J]. Northern Journal of Applied Forestry, 2004, 21(2):83-92.
[20]	曾伟生, 唐守正. 非线性模型对数回归的偏差校正及与加权回归的对比分析[J]. 林业科学研究, 2011, 24(2):137-143.
[21]	Wang M, Kane M, Borders B, et al. Direct variance-covariance modeling as an alternative to the traditional guide curve approach for prediction of dominant heights[J]. Forest Science, 2014, 60(4):652-662
[22]	曾伟生. 加权回归估计中不同权函数的对比分析[J]. 林业资源管理,2013,05:55-61.
[23]	曾伟生, 唐守正. 立木生物量方程的优度评价和精度分析[J]. 林业科学,2011,11:106-113.
[24]	骆期邦, 宁辉, 贺东北, 等. 二元立木材积动态模型研究[J]. 林业科学研究, 1992, 5(3):263-270.

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

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Compatible Tree Volume Equations and Heteroscedasticity for Dahurian Larch in Different Region of Daxing'anling

1. College of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, China

Received Date: 2015-09-10

Abstract: [Objective] Making a detailed comparative analysis of compatible volume models in different regions and different heteroscedasticity correction methods, developing compatible volume equations to estimate different regions for Dahurian larch (Larix gmelini Rupr.) in Daxing'anling.[Method] Regional differences in volume models were examined and tested using the nonlinear extra sum of squares method (F-test). Weighted regression was used to decrease the heteroscedasticity of volume equations in three regions using variety forms of weight functions.[Result] The results indicated that the volume models were significantly different among different regions (PF(x), 1/D4.99, 1/D3.38 for region 1(-0.11, 0.97), region 2(0.04, 0.08), and region 3(1.04, 0.93) respectively.[Conclusion] Individual tree volume model is a major component of forest inventory and growth and yield model. Prediction errors of compatible volume models were within ±3% in three different regions. Compatible volume models should consider the phenomena of heteroscedasticity, and the optimal weight functions of individual tree volume models don't have a uniform format. To get the stability of parameters estimation, different weight functions should be analyzed in the process of the weighted regression.

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Reference (24)

[1]	Amateis R L, Burkhart H E. Cubic-foot volume equations for loblolly pine trees in cutover, site-prepared plantations[J]. Southern Journal of Applied Forestry, 1987, 11(4):190-192.
[2]	Fowler G W. Individual tree volume equations for red pine in Michigan[J]. Northern Journal of Applied Forestry, 1997, 14(2):53-58.
[3]	曾伟生. 杉木相容性立木材积表系列模型研建[J]. 林业科学研究, 2014, 27(1):6-10.
[4]	张会儒, 唐守正. 与材积兼容的生物量模型的建立及其估计方法研究[J]. 林业科学研究, 1999, 12(1):53-59.
[5]	Snorrason A, Einarsson S F. Single-tree biomass and stem volume functions for eleven tree species used in Icelandic forestry[J]. Icelandic Agricultural Sciences, 2006, 19:15-24.
[6]	Brooks J R, Wiant H V. Ecoregion-based local volume equations for Appalachian hardwoods[J]. Northern Journal of Applied Forestry, 2008, 25(2):87-92.
[7]	Case B S, Hall R J. Assessing prediction errors of generalized tree biomass and volume equations for the boreal forest region of west-central Canada[J]. Canadian Journal of Forest Research, 2008, 38(4):878-889.
[8]	胥辉. 一种与材积相容的生物量模型[J]. 北京林业大学学报, 1999, 21(5):32-36.
[9]	曾鸣, 聂祥永, 曾伟生. 中国杉木相容性立木材积和地上生物量方程[J]. 林业科学, 2013, 49(10):74-79.
[10]	Tang S, Li Y, Wang Y. Simultaneous equations, error-in-variable models, and model integration in systems ecology[J]. Ecological Modelling, 2001, 142(3):285-294.
[11]	Tang S, Wang Y. A parameter estimation program for the error-in-variable model[J]. Ecological Modelling, 2002, 156(2):225-236.
[12]	Fortin M,Daigle C,Ung C, et al. A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling[J]. European Journal of Forest Research, 2007, 126:573-585.
[13]	McRoberts R, Westfall J. Effects of uncertainty in model predictions of individual tree volume on large area volume estimates[J]. Forest Science, 2014, 60(1):34-42
[14]	吴明山, 胥辉, 叶江霞. 兴安落叶松材积模型中的异方差研究[J]. 山东林业科技, 2010, 40(2):14-17.
[15]	Huang S, Price D, Titus S J. Development of ecoregion-based height-diameter models for white spruce in boreal forests[J]. Forest Ecology and Management, 2000, 129(1):125-141.
[16]	Peng C, Zhang L, Liu J. Developing and validating nonlinear height-diameter models for major Tree species of Ontario's boreal forests[J]. Northern Journal of Applied Forestry, 2001, 18(3):87-94.
[17]	夏忠胜, 曾伟生, 朱松, 等. 贵州省人工杉木立木材积方程研建[J]. 北京林业大学学报, 2012, 34(1):1-5.
[18]	Zhang L, Peng C, Huang S, et al. Development and evaluation of ecoregion-based jack pine height-diameter models for Ontario[J]. The Forestry Chronicle, 2002, 78(4):530-538.
[19]	Peng C, Zhang L, Zhou X, et al. Developing and evaluating tree height-diameter models at three geographic scales for black spruce in Ontario[J]. Northern Journal of Applied Forestry, 2004, 21(2):83-92.
[20]	曾伟生, 唐守正. 非线性模型对数回归的偏差校正及与加权回归的对比分析[J]. 林业科学研究, 2011, 24(2):137-143.
[21]	Wang M, Kane M, Borders B, et al. Direct variance-covariance modeling as an alternative to the traditional guide curve approach for prediction of dominant heights[J]. Forest Science, 2014, 60(4):652-662
[22]	曾伟生. 加权回归估计中不同权函数的对比分析[J]. 林业资源管理,2013,05:55-61.
[23]	曾伟生, 唐守正. 立木生物量方程的优度评价和精度分析[J]. 林业科学,2011,11:106-113.
[24]	骆期邦, 宁辉, 贺东北, 等. 二元立木材积动态模型研究[J]. 林业科学研究, 1992, 5(3):263-270.

Compatible Tree Volume Equations and Heteroscedasticity for Dahurian Larch in Different Region of Daxing'anling

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通讯作者: 陈斌, bchen63@163.com

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Compatible Tree Volume Equations and Heteroscedasticity for Dahurian Larch in Different Region of Daxing'anling

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