Establishment of basal diameter relevant models and volume table for Quercus variabilis in northern China.

Based on the data of 149 analytical sample trees, we established three well-performed independent models: 1) a linear model between diameter at breast height outside bark (DBHob) and basal diameter inside bark (BDib) (DBHob-BDib), 2) a power function model between DBHob and tree height (H) (DBHob-H), and 3) a linear model between DBHob, H and volume inside bark (Vib) (DBHob, H-Vib) based on the variables after natural logarithmic transformation. Then, based on these three independent models, a compatible BDib-DBHob-H-Vib model system was established with the method of simultaneous equations with error variables, and thus compatible volume equations (table) based on BDib-DBHob and DBHob-H were obtained. According to the results of six statistical indexes, residual plots, Shapiro Wilk tests and independent data tests for each model, heteroscedasticities were not detected in these models and residuals of these models followed a normal distribution. Ranges of residuals of these models in fitting and testing phases were very narrow, compared with the ranges of dependent variables. The volume table had promising precisions, thus they could be used for estimating Quercus variabilis volume and can provide support for dealing with illegal logging or deforestation cases of cork oak forests in northern China. As an important component of forest growth and yield model system, DBHob-H model can be used to estimate average tree height given a known DBHob, and on this basis, forest volume and biomass could be calculated eventually. Therefore, the DBHob-H model is very important in forest survey. We should point out that models established in this study are only applicable for cork oak trees in northern China with a DBHob range of 5-21 cm.