Development of Crown Profile Models for Chinese Fir Using Non-linear Mixed-Effects Modelling

Crown profile models are key components of growth and yield models and are crucial for estimating the crown volume and constructing 3D visualization of trees. We used a total of 431 trees collected from 98 pure even-aged temporary sample plots established in Fujian Province to develop crown profile models of Chinese fir (Cunninghamia lanceolata).To describe the shape of tree crowns more accurately, significance tests of the effects of different stand conditions (stand age, site index, and stand density) on crown shape were conducted with one-way analysis of variance (ANOVA). Multiple comparisons based on the ANOVA results were used to classify the crown data into three groups according to stand age: Group I (young forest), Group II (medium forest), and Group III (nearly mature and mature forest). We analysed the relationships between the crown variables and stand variables and used the reparameterization approach to develop three optimal crown profile models for different age groups. Stand variables (such as stand density) further improved the prediction efficacy of the models. Considering the correlation between repeated measurement data for the same tree crown, the non-linear mixed-effects modelling (NLME) method was used to account for autocorrelation. The determination coefficients (R2) of the above three optimal models fitted by the non-linear mixed-effects approach were 0.9214, 0.9398 and 0.9129, and their Root Mean Squared Errors (RMSEs) were 0.1246, 0.1409 and 0.1786, respectively. The determinant coefficients (R2) of the three models fitted by the nonlinear least squares (NLS) approach were 0.9015, 0.8794 and 0.8930, and their RMSEs were 0.1395, 0.2102 and 0.1878, respectively. The results indicated that the predicted accuracy was significantly increased by using non-linear mixed effects modelling compared with the NLS method.