Using Measurement Error Modeling Method to Establish Compatible Single-Tree Biomass Equations System

ZENG Wei-sheng; TANG Shou-zheng

A system of equations for total biomass and the components must be compatible or additive, that is, the predicted values from the component biomass equations should add up to the predicted value from the total biomass equation. Based on the above-ground biomass data of Masson pine (Pinus massoniana) of southern China, the compatible systems of single-tree biomass equations for total above-ground biomass and the four components (stem wood, stem bark, branch, and foliage) were established using the error-in-variable modeling method in this paper. Firstly, starting from the analysis of properties of the component proportions to total biomass, two alternative approaches, controlling jointly from level to level by ratio functions and controlling directly under total biomass by proportion functions, were presented to design the compatible system of biomass equations based on the above-ground biomass which could be estimated independently apart from the system or estimated simultaneously in the system. It was showed that the approach controlling jointly by ratio functions was same effective as the one controlling directly by proportion functions, and the method that total above-ground biomass being estimated independently had almost the same prediction precision as that being estimated simultaneously. Secondly, the goodness-of-fit between biomass models with one variable and two or three variables were compared, and the results showed that the standard error of estimate (SEE) and mean prediction error (MPE) would decreased with increasing explainable variables, but the contribution to prediction precision was not high. Finally, the properties of the proportions of four components to total above-ground biomass were analyzed, and the results showed that the proportion of stem wood would increased with growing diameter, the proportions of stem bark and foliage would decreased with growing diameter, and the proportion of branches might be relatively stable. From the compatible system of biomass equations established in this paper, the prediction precision of total above-ground biomass estimate was higher than 95%, and the precision of foliage biomass estimate was the lowest but higher than 85%.

1. Research Institute of Forest Resources Information Techniques, Chinese Academy of Forestry, Beijing 100091, China

Received Date: 2010-04-10

Abstract: A system of equations for total biomass and the components must be compatible or additive, that is, the predicted values from the component biomass equations should add up to the predicted value from the total biomass equation. Based on the above-ground biomass data of Masson pine (Pinus massoniana) of southern China, the compatible systems of single-tree biomass equations for total above-ground biomass and the four components (stem wood, stem bark, branch, and foliage) were established using the error-in-variable modeling method in this paper. Firstly, starting from the analysis of properties of the component proportions to total biomass, two alternative approaches, controlling jointly from level to level by ratio functions and controlling directly under total biomass by proportion functions, were presented to design the compatible system of biomass equations based on the above-ground biomass which could be estimated independently apart from the system or estimated simultaneously in the system. It was showed that the approach controlling jointly by ratio functions was same effective as the one controlling directly by proportion functions, and the method that total above-ground biomass being estimated independently had almost the same prediction precision as that being estimated simultaneously. Secondly, the goodness-of-fit between biomass models with one variable and two or three variables were compared, and the results showed that the standard error of estimate (SEE) and mean prediction error (MPE) would decreased with increasing explainable variables, but the contribution to prediction precision was not high. Finally, the properties of the proportions of four components to total above-ground biomass were analyzed, and the results showed that the proportion of stem wood would increased with growing diameter, the proportions of stem bark and foliage would decreased with growing diameter, and the proportion of branches might be relatively stable. From the compatible system of biomass equations established in this paper, the prediction precision of total above-ground biomass estimate was higher than 95%, and the precision of foliage biomass estimate was the lowest but higher than 85%.

HTML

Reference (18)

[1]	Tomppo E, Gschwantner T, Lawrence M,et al.. National Forest Inventories: Pathways for Common Reporting[M]. Springer, New York, 2010
[2]	Jenkins J C, Chojnacky D C, Heath L S, et al.. National-scale biomass estimators for United States tree species[J]. For Sci,2003, 49(1):12-35
[3]	FAO. Global Forest Resources Assessment 2005: Progress Towards Sustainable Forest Management. FAO Forestry Paper 147 . Food and Agriculture Organization of the United Nations, Rome,2006
[4]	骆期邦,曾伟生,贺东北,等.立木地上部分生物量模型的建立及其应用研究[J]. 自然资源学报,1999,14(3): 271-277
[5]	唐守正,张会儒,胥辉.相容性生物量模型的建立及其估计方法研究[J].林业科学,2000,36(专刊1):19-27
[6]	Parresol B R. Additivity of nonlinear biomass equations[J]. Can J For Res,2001, 31: 865-878
[7]	Bi H, Turner J, Lambert M J. Additive biomass equations for native eucalypt forest trees of temperate Australia[J]. Trees, 2004,18: 467-479
[8]	Tang S Z, Li Y, Wang Y H. Simultaneous equations, error-in-variable models, and model integration in systems ecology[J]. Ecological Modelling, 2001,142: 285-294
[9]	Tang S Z, Wang Y H. A parameter estimation program for the error-in-variable model[J]. Ecological Modelling,2002, 156: 225-236
[10]	唐守正,李勇.生物数学模型的统计学基础[M].北京:科学出版社,2002
[11]	唐守正,郎奎建,李海奎.统计和生物数学模型计算(ForStat教程)[M].北京:科学出版社,2008
[12]	李永慈,唐守正,李海奎,等.用度量误差模型方法编制相容的生长过程表和材积表[J].生物数学学报,2004,19(2): 199-204
[13]	李永慈,唐守正.带度量误差的全林整体模型参数估计研究[J].北京林业大学学报,2006,28(1): 23-27
[14]	曾伟生.再论加权最小二乘法中权函数的选择[J].中南林业调查规划,1998,17(3):9-11
[15]	曾伟生,骆期邦,贺东北.论加权回归与建模[J].林业科学,1999,35(5):5-11
[16]	胥辉.生物量模型方差非齐性研究[J].西北林学院学报,1999,19(2):73-77
[17]	张会儒,唐守正,胥辉.关于生物量模型中的异方差问题[J].林业资源管理,1999(1):46-49
[18]	Parresol B R. Assessing Tree and Stand Biomass: A Review with Examples and, Critical Comparisons[J]. For Sci, 1999,45(4): 573-593

Using Measurement Error Modeling Method to Establish Compatible Single-Tree Biomass Equations System

Abstract

References

Proportional views

通讯作者: 陈斌, bchen63@163.com

Proportional views