Methodology On Modeling Of Single-tree Biomass Equations For National Biomass Estimation In China

Since forest ecosystem plays an irreplaceable role in regulating global carbon balance and mitigating global climate change, the forest biomass monitoring is becoming more important all over the world. Many national governments and international organizations focus increasing emphasis on forest biomass monitoring in large scale regions. It is fundamental for monitoring and assessment of national forest biomass to develop generalized single-tree biomass models suitable for large scale forest biomass estimation. Based on the situation of national forest resources monitoring, and aiming at serving national forest biomass monitoring in China, the technical methodologies on modeling of single-tree biomass equations suitable for national forest biomass estimation, involving classification of modeling population, determination of sample structure, collection of sample trees, selection of regression procedure, presentation of evaluation indices, establishment of above- and below-ground biomass equations, were studied systematically using statistical analysis and bio-mathematical modeling methods developed in modern times. A series of achievements were obtained, and several breakthroughs were made in this study. The results and conclusions will provide technical support for the forthcoming effort on modeling of single-tree biomass equations in China.The following innovations and breakthroughs have been obtained: 1) viewing from implementing national forest biomass monitoring, the schemes on classifying modeling population and determining sample structure for building up national single-tree biomass equations were presented for the first time; 2) logarithmic regression and the bias correction for non-linear model such as biomass equation were studied, the immanent cause producing bias in logarithmic regression was analyzed, and a new correction factor was presented; 3) based on the basic assumptions of linear regression estimation and related formulas of confidence intervals for prediction, the approach to estimate confidence intervals of conditional mean and single predicted value of tree biomass models was provided through transforming model expression and eliminating heteroscedasticity; 4) from the random sub-sampling tests by jackknife method, it was claimed that applicable validation from another set of samples was not necessary which would waste information and increase cost, instead, all sample trees (not being classified into fit samples and validation samples) should be used for establishing single-tree biomass models; 5) an approach to develop compatible tree volume and above- ground biomass equations and biomass conversion functions, using the error-in-variable simultaneous equations (also called error-in-variable modeling method),?was?presented for the first time; 6) the compatible systems of single-tree biomass equations for total above-ground biomass and the four components (stem wood, stem bark, branches, and foliage) were established using the error-in-variable simultaneous equations, and the relations and properties of two alternative approaches, controlling jointly from level to level by ratio functions and controlling directly under total biomass by proportion functions, were analyzed in depth; 7) an approach to develop compatible above- and below-ground biomass equations and root-shoot ratio function, using the error-in-variable simultaneous equations,?was?presented for the first time; 8) a procedure to build generalized single-tree biomass equations applying to national and regional forest biomass estimation was established using mixed-effects modeling method, which provided an effective approach to solve the compatibility of forest biomass estimates among the different scales; 9) accounting that single-tree biomass equations with constant parameters within the range of size classes may result in obvious biased estimation for small young trees, the subsection modeling approach was presented to improve the estimation of tree biomass; 10) considering that the theoretical allometric biomass model developed by West et al (1997, 1999) was statistically different from the empirical one, a new generalized biomass model M=0.3pD^7/3 was presented.From the results and achievements in this study, it was mainly concluded that: 1) The above-ground biomass equation should be developed using error-in-variable simultaneous equations. Firstly, the above-ground biomass equation and biomass conversion function compatible with tree volume should be established; then based on the above-ground biomass equation developed afore-mentioned, a compatible system of simultaneous equations for total above-ground biomass and the four components (stem wood, stem bark, branches, and foliage) would be established. 2) The below-ground biomass equation and root-shoot ratio function compatible with above-ground biomass equation should be developed using error-in-variable simultaneous equations; when less sample trees was selected for below-ground biomass measurement,?the root-shoot ratio function should be used to estimate below-ground biomass together with above-ground biomass equation built up on more sample trees. 3) Because the contributions of explainable variables to object variable in linear biomass models were simply accumulative, it was inevitable to produce unreasonable prediction such as negative biomass value. Considering the statistical indices together for comparison and evaluation, linear models were worse than nonlinear ones; thus nonlinear models should be used for developing national single-tree biomass equations. 4) For nonlinear models with heteroscedasticity such as biomass equations, logarithmic regression with effective bias correction would be equivalent to weighted regression. Since the nonlinear regression estimation has been used very commonly, weighted regression should be suggested to estimate the parameters of biomass equations. 5) The one-variable model based on diameter at breast height has explained more than 95% variation of above-ground biomass. When more explainable variables were taken into account, the prediction precision of estimates would increase in some extent, but meanwhile, the workload in field would raise and the measurement errors would accumulate. So one-variable model was suggested to be applied to estimate forest biomass in national forest resources inventory; 6) To meet the needs of national and provincial monitoring and assessment of forest biomass, the generalized single-tree biomass equations appropriate for national and regional forest biomass estimation could be established using mixed model or dummy variable model method, which could insure the compatibility between national and regional equations; 7) To establish single-tree biomass equation suitable to both trees with diameter more than 5cm and saplings with diameter less than 5cm, and to ensure the biomass estimation unbiased for young trees with small diameter, nonlinear regression equation with intercept or segmented modeling approach could be used to improve the regression. Because the biomass proportion of small young trees and saplings to forest biomass would be low, the commonly used nonlinear biomass equations might be adequate if the bias was neglectful; 8) The proportions of four components to total above-ground biomass showed various changing patterns: proportion of stem wood would increase with growing diameter, the proportions of stem bark and foliage would decrease with growing diameter, and the proportion of branches might be relatively stable or slightly decreased. The root-shoot ratio might mainly depend upon diameter of the tree, and would increase gradually with growing diameter.