ObjectiveThe tree volume equation has been widely used in studying forest productivity, biomass and carbon storage. Therefore, improving the prediction precision of tree volume has always been an important task for forestry model researchers. Two-variable and three-variable volume equations were established based on different form quotients of the trunk, and compared and tested the predictive effects for Pinus sylvestris var. mongolica in Daxing^,anling Mountains of northeastern China to improve the prediction precision of traditional tree volume to a new level.

MethodUsing the 15 different form quotients of the trunk, two-variable and three-variable volume equations were established based on the traditional one-variable and two-variable volume equations, respectively, and compared with the traditional one-variable and two-variable volume equations. All models were fitted using GNLS in S-PLUS. And the optimal form quotient model was selected. Variance functions (power function, constant plus power function and exponential function) were incorporated into generalized models to decrease heteroscedasticity. And the precision of different individual volume models was evaluated using four factors: mean absolute bias (MAB), mean percentage of bias (MPB), root mean square error (RMSE), and coefficient determination (R²). Finally, the prediction precision of four kinds of equations in different diameter classes was compared by the method of different diameter classes testing.

ResultThe results showed that the two-variable model based on 70% of the relative height had the best fitting effect, and the three-variable model based on the relative height of 50% was the best. The model test results showed that based on the traditional one-variable model, the RMSE, MAB and MPB of the model after adding form quotient were reduced by 33.7%, 30.7%, and 29.9%, respectively. Based on the traditional two-variable model, the RMSE, MAB and MPB of the model after adding form quotient, were reduced by 70.5%, 70.9% and 71.2%, respectively. From evaluation results of different diameter classes testing, for small and medium diameter classes, the order of test precision was: model (13) > model (2) > model (12) > model (1); for large diameter classes, the order of test precision was: model (13) > model (12) > model (2) > model (1).

ConclusionThe form quotient is an important index of stem form. The introduction of form quotient factor into traditional tree volume model can improve the prediction precision of tree volume. Therefore, the three-variables volume model with form quotient factor is recommended for estimating tree volume of Pinus sylvestris var. mongolica, especially for medium and large diameter trees.