A generalized nonlinear mixed-effects height to crown base model for Mongolian oak in northeast China

Tree height to crown base (HCB) is an important variable commonly included as one of the predictors in growth and yield models that are the decision-support tools in forest management. In this study, we developed a generalized nonlinear mixed-effects individual tree HCB model using data from a total of 3133 Mongolian oak (Quercus mongolica) trees on 112 sample plots allocated in Wangqing Forest Bureau of northeast China. Because observations taken from same sample plots were highly correlated with each other, the random effects at the levels of both sample plots and stands with different site conditions (blocks) were taken into consideration to develop a two-level nonlinear mixed-effects HCB model. The results showed that the significant predictors included total tree height, diameter at breast height (DBH), dominant height, and total basal area of all trees with DBH larger than a target tree per sample plot. Modelling the random effects at block level alone led to highly significant correlation among the residuals. The correlation significantly decreased when the random effects were modeled at both block and sample plot levels. Four alternatives of HCB sampling designs (selecting the largest, medium-size and smallest trees, and the randomly selected trees) and eight sample sizes (one to eight trees) for calibrating the mixed effects HCB model using an empirical best linear unbiased prediction approach were examined. It was found that the prediction accuracy of HCB model increased with increasing the number of sample trees for each alternative, but the largest increase occurred when four randomly selected sample trees were used to estimate the random effects. Thus, HCB measurements from four randomly selected trees per sample plot should be used to estimate the random effects of the model.