Construction Of Taper Equation For Larix Olgensis Based On Two-level Nonlinear Mixed Effects Model

Based on the stem taper data of 177 artificial Larix olgensis trees,which from from 31 per manent sample plots in Mengjiagang forest farm,Dongjingcheng forest farm and Linkou forest farm in Heilongjiang Province.The optimal model was selected as the basic model,and crown characteristic variables were introduced by reparameterization method to analyze the influence of crown characteristic factors on the taper.On the basis of the crown characteristic factors mo del,consider the effects of plot and wood effect the taper to builde the high-precision cutting eq uation of Larix olgensis.With the secondary sampling of the mixed effect model,this study ana lyzed the accuracy of the taper model by different sampling strategies（Strategy I:the global op timal plan that does not limit the sampling position;Strategy II:the plan with a relatively high i s limit of less than 0.1）.The contributions and conclusions of this study are as follows:（1）Among the different type of taper equations,the predictable accuracy of variable-form taper equation was better than segmented taper equation and single taper models.And the Koza k（2004）equation as the best fitting effect(²₍（6（6）=0.9886,RMSE=0.8622）was selected as the ba sic model.（2）The crown characteristic factors can improve the accuracy of taper function.Among th em,the crown ratio model equation has the best fitting results and the model parameters were a ll significant at the 5%significance level.The tree has different crown ratio,and the taper of th e tree is different,the taper of the tree gradually increase with increasing crown ratio.（3）Base on the crown ratio model,the sample plot effect and the sample tree effect improv ed the accuracy of the model.The exponential function and CAR（1）structure were used to solv e the heteroscedasticity and autocorrelation problems in the taper equation.The goodness-of-fit for the mixed-effect models were²₍(6（6）=0.9941,RMSE=0.6231 that was better than the basic mo del(²₍（6（6） increased by 0.4%,RMSE decreased by 24.6%）.（4）When using different sampling strategy for model prediction,the Strategy I showed the best result（MAE was 0.47 cm,MAPE was 4.62%）,when the sampling number is 5.For Strate gy II,there were little difference on predicting accuracy with different sampling numbers（the r ange of MAE was 0.5203～0.5366,the range of MAPE was 5.14%～5.22%）,but still better than the basic model.（5）When different sampling plan are used for volume prediction,plan I showed higher pre diction accuracy when the sampling number is 5（MAE is 0.00796m³,MAPE is 3.28%）.There is no significant difference in volume prediction accuracy between different sampling numbers in plan II（MAE range was 0.01292～0.01350,MAPE range was 4.36%～4.52%）.（6）The two-level mixed-effects model,including plot effect and tree effect,was better tha n the basic model,and it will be suitable for predicting the stem shape changes of Larix olgensi s.The results will provide a better method for precisely predicting the tree volume of Larix olge nsis.