含随机效应和度量误差的生物量相容性方程系统研究

构建生物量相容性方程系统是生物量建模技术中的一项重要基础工作。迄今为止，已提出了多种建模方法，但实际应用时，发现由这些方法得到的生物量相容性方程系统只适用于模型参数不受随机因素影响的实验条件。然而现实中树木各分项生物量常受一些因子的随机影响，如立地条件、生长状况和遗传等。当方程系统中部分或全部参数考虑随机效应时（此时的方程系统为混合效应模型联立方程组），已有的方程系统不再适用。此外，方程系统中除各分项生物量（自变量）含有度量误差外，其它林分或树木因子（因变量）也可能存在一定程度的度量误差。为此，本项目重点解决三个问题：（1）在已有生物量相容性方程系统研究基础上，考虑方程系统中参数受随机因素的影响，并推导出可行的参数估计算法。（2）在此基础上，进一步解决方程中自变量和因变量同时含有度量误差而引起的参数估计偏差问题。（3）基于以上研究成果，首次实现考虑随机效应的无偏的生物量相容性方程系统构建。

Developing a system of compatible biomass equations is important and basic work for biomass modelling. So far, many methods have been proposed to develop systems of compatible biomass equations. However, all the obtained systems are adaptable only for the experimental conditions in which random effects are not involved. In fact, the random effects of factors such as site types, regions and genetic characteristics on each component of tree biomass may be very significant and cannot be ignored in the practice. When there are the random effects (in the case typical mixed-effects equations should be taken into account), the existing systems of compatible biomass equations do not work well. In addition to each component of tree biomass, the observed values of stand or tree variables as independent variables of the equation systems also contain measurement errors. The consideration of both random effects and measurement errors in development of compatible biomass equation systems will be challenging. For the purposes, this research aims at: 1) proposing a feasible parameter estimation algorithm for the existing equation system in which random effects on parameters are added; 2) after that, searching for the solution of the biased parameter estimation caused by the measurement errors in the observed values of both dependent and independent variables; and 3) following is the development of an unbiased system of compatible biomass equations considering both random effects and measurement errors.