Nonlinear mixed-effects height to crown base and crown length dynamic models using the branch mortality technique for a Korean larch (Larix olgensis) plantations in northeast China

Korean larch (Larix olgensis) is one of the main tree species for afforestation and timber production in northeast China. However, its timber quality and growth ability are largely influenced by crown size, structure and shape. The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots, but crown dynamic models has seldom been constructed. Therefore, this study aimed to develop height to crown base (HCB) and crown length (CL) dynamic models using the branch mortality technique for a Korean larch plantation. The nonlinear mixed-effects model with random effects, variance functions and correlation structures, was used to build HCB and CL dynamic models. The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China. The results showed that HCB progressively increases as tree age, tree height growth (HT growth) and diameter at breast height growth (DBH growth). The CL was increased with tree age in 20 years ago, and subsequently stabilized. HT growth, DBH growth stand basal area (BAS) and crown competition factor (CCF) significantly influenced HCB and CL. The HCB was positively correlated with BAS, HT growth and DBH growth, but negatively correlated with CCF. The CL was positively correlated with BAS and CCF, but negatively correlated with DBH growth. Model fitting and validation confirmed that the mixed-effects model considering the stand and tree level random effects was accurate and reliable for predicting the HCB and CL dynamics. However, the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation, and the fitting precision of the models was reduced. Therefore, from the point of view of application, we should take care to avoid setting up over-complex models. The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.