A Nonlinear Mixed-Effects Height-Diameter Model with Interaction Effects of Stand Density and Site Index for Larix olgensis in Northeast China

Tree height is a basic input variable in various forest models, such as growth and yield models, biomass models, and carbon budget models, which serve as very important tools for the informed decision-making in forestry. The height-diameter model is the most important component of the growth and yield models and forest simulators. We developed the nonlinear mixed-effects height-diameter model with the interaction effects of stand density and site index introduced using data from 765 Larix olgensis trees in Jingouling forest farm of the Wangqing Forest Bureau in northeast China. Among the various basic versatile functions evaluated, a simple exponential growth function fitted the data adequately well, and this was then expanded through the introduction of the variables describing the interaction effects of the stand density and site index on the height-diameter relationship. Sample plot-level random effects were included into this model through mixed-effects modeling. The results showed that the random effect of the stand density on the height-diameter relationship was substantially different at different classes of the site index, and the random effect of the site index was different for the different stand density classes. The nonlinear mixed-effects (NLME) height-diameter model coping with the interaction effects of the stand density and site index had a better performance than those of the NLME models with the random effect of the single variable of stand density or site index. To conclude, the inclusion of the interaction effects of stand density and site index could significantly improve the prediction accuracy of the height-diameter model for Larix olgensis Henry. The proposed model with the interactive random effects included can be applied for the accurate prediction of Larix olgensis tree height in northeast China.