山本和藏材积方程参数特征

Characterisation of the parameters of the Yamamoto-Kazuhide volume equation

【目的】山本和藏方程是二元立木材积模型中应用最广泛的模型,山本式的参数较好地体现了材积三要素之间的关系,解析推导山本式的结构特征,分析现有山本式材积模型的应用现状,为山本式的理论研究提供了基础,为精准测算林分蓄积量提供了理论依据。【方法】基于山本和藏方程,引入形状指数r采用多元函数偏导数的方法对胸高形数与胸径和树高之间的关系式进行求导,结合二分法求函数的零点,推导山本式参数的取值范围。以170个现有的山本式材积模型参数为研究对象,利用方差分析和多重比较Scheffe法对数据进行差异化分析,对比不同地区及树种组之间山本式的参数值。【结果】1)在h>1.3 m时,胸高形数是关于胸径和树高的减函数,胸高形数随着胸径和树高的增加而减少。2)山本式的参数存在取值范围,且现行的170个山本式二元材积方程中参数b取值范围异常的比例达5%,参数c异常的比例达43%。3)由箱线图可视化结果可知,山本式的参数存在离散值;北方的山本式参数值跟南方相比较为集中;阔叶树种的参数值比针叶树种的分布更为平均。【结论】山本式的参数存在取值范围,a>0,b<2,c<1。山本式的实际运用中存在很多参数偏离取值范围的情况,给材积的预估带来了偏差。因此研究山本和藏方程的理论推导,考虑山本式的参数取值范围,对二元材积表的编制、林分蓄积量预估以及森林资源监测与管理具有重要意义。

【Objective】Among the standard volume models,the Yamamoto-Kazuhide equation was the most frequently used,the Yamamoto-Kazuhide equation’s parameters precisely reflected the correlation between the three elements of volume,this study aimed to analytically deduce the structural features of the Yamamoto-Kazuhide equation and investigate the current status of the applications of the existing Yamamoto-Kazuhide equation models,which created the foundation for the study of the Yamamoto-Kazuhide equation theoretically and as a theoretical basis for precisely measuring stand volume.【Method】Based on the Yamamoto-Kazuhide equation,the relationship equation between the breast-height form factor,diameter at breast height,and tree height was derived using the approach of partial derivatives of multivariate functions and the shape index r.combined with the Bisection method to find the zero point of the function,and to deduce the range of values of the parameters of the Yamamoto-Kazuhide equation.The 170 existing Yamamoto-Kazuhide equation volume model parameters were used as the research object,and the data were differentiated using ANOVA and multiple comparison Scheffe method to compare the parameter values of Yamamoto-Kazuhide equation between different regions and tree species groups.【Result】1)When h>1.3 m,the breast-height form factor was a decreasing function of diameter at breast height and tree height,and the breast-height form factor decreases with increasing diameter at breast height and tree height.2)The Yamamoto-Kazuhide equation had parameter ranges,and the existing 170 Yamamoto-Kazuhide binary equations exhibit anomalied in the parameter b range of values in 5%of cases and the parameter c range of values in 43%of cases.3)The Box-plot visualization result showed that the parameters of the Yamamoto-Kazuhide equation had discrete values,and the parameter values in the northern regions were more concentrated compared to those in the southern regions;the parameter values of broad-leaved tree species were more evenly distributed than those of coniferous tree species.【Conclusion】The parameters of the Yamamoto-Kazuhide equation have a range of values:a>0,b<2,c<1.The practical application of the Yamamoto-Kazuhide equation has many parameters deviating from the range of values,which brings bias to the estimation of timber volume.Therefore,it is of great significance to study the theoretical derivation of the Yamamoto-Kazuhide equation and to consider the range of values of the parameters of the Yamamoto-Kazuhide equation for the compilation of the standard volume tables,estimation of stand volume,and monitoring and management of forest resources.