Nonlinear Mixed-effects Modeling Of Variable Exponent Taper Equations With Density For Chinese Fir

Chinese fir(Cunninghamia lanceolata [Lamb.] Hook)is important native coniferous timber species in southern China.Currently,the area and stocking volume lag of Chinese fir plantation have reached the main position of the national forest.Therefore,it is necessary to accurately evaluate volume of the Chinese fir plantation in the national forest resources inventory.The taper equation play a very important role in accurately predicting the diameter and volume of the bole.At present,there are few studies on the systematic comparative analysis of the basic taper equation.In particular,the construction of the variable taper equation and the variable taper equation with density for Chinese fir is rare.In this study,based on the density test stand of Chinese fir in Jiangxi,the variable taper equation with initial density and volume model were developed using the nonlinear mixed effects.The main conclusions are as follows:(1)The predictable accuracy of variable-form taper equation is better than segmented taper equation and single taper models.The fit statistics is no more obvious between the variable taper equations.Four variable-exponent taper models that developed by Zeng(1997),Bi(2000),Kozak(2004),Sharma(2004),respectively,were selected as basic model.(2)The nonlinear mixed effects(NLME)models with the plot level,the tree level and the nested two level model is established for the selected basic model.The nonlinear mixed effects models significantly improves the fitting performance.The plot levels NLME model improved the with 0.0016~0.0020 compared to nonlinear regressions.But the plot levels NLME model did not remove the residual autocorrelation.The tree levels and nested two levels NLME model improved the with 0.0104~0.0117 compared to the plot levels NLME model,the results showed that the correlations within each tree can be largely overcome.Variable-exponent taper models developed by Kozak(2004)showed the best performance for the NLME model with nested two levels and the tree levels.The tree levels Kozak(2004)NLME model was selected because its structure simpler than the nested two levels NLME model.(3)On the basis of the conclusion(2),variable taper equations with stand density for Chinese fir were established.After adding the density factor in the taper equation,the fitting accuracy of the taper equation is improved with the high adjusted determination coefficient of 0.9945.The boles at different densities have different taper,and the taper of the bole gradually decreases with increasing density.For the same difference between stand densities,however,the difference in bole diameter between lower and higher stand densities diminishes as stand density increases.(4)The Chinese fir volume is predicted used variable taper equation with the stand density.The result is that the Bias,RMSE,MAD and Bias% of variable taper equation with the stand density is lower than standard volume table and sample taper equation integral quadrature.Predictive volume accuracy is poor in the range of low height to diameter ratio and breast-height form factor for three kinds of volume prediction methods.In the three methods,the variable exponent taper equation with density predicts the highest volume accuracy.