Characterisation of the parameters of the Yamamoto-Kazuhide volume equation
[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.
the Yamamoto-Kazuhide equationthree elements of volumestem volumepartial derivativeANOVA
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NSTL
万方数据
