Comparing different height-diameter models of Pinus sylvestris var. mongolica in sandy land

Objective  To compare the accuracy of different height(H)-diameter (D) models to determine the optimal models for Pinus sylvestris var. mongolica in Zhanggutai area.

Method  Sibbesen model was used as the basic model. Dominant height (H_T), stand basal area (A_B), and quadratic mean diameter (D_QM) with different combinations were added into Sibbesen model. We established one basic, three generalized, one basic mixed and three generalized mixed H-D models. The accuracies of population-averaged prediction (FPA) of fixed effects models, and mean response prediction (MPA) and specific-plot prediction (MPS) of mixed effects models were compared. For mixed models, two sampling designs, random sampling and medium-diameter tree sampling were used for random parameters estimation, and the relationship between MPS accuracy and sample size was analyzed.

Result  In four fixed H-D models, the generalized model with H_T and A_B has the highest prediction precision. Akaike’s information criterion (AIC) is 2 167.7. Bayesian information criterion (BIC) is 2 196.3. Models with the same predictor variables have precision in order of MPS> FPA>MPA, and models withD as the only variable have the largest variation among three types of prediction. There are little difference in prediction accuracy among generalized models, generalized mixed models and basic mixed model. Using three randomly selected sample trees per plot to estimate random parameters of basic mixed model results in the highest model precision based on the validation data, and MAE and RMSE decrease by 57.97% and 57.63% respectively. The accuracies of generalized mixed models do not change significantly with the increase of sample size.

Conclusion  Both generalized model including H_T and A_B and basic mixed model can well predict tree height for P. sylvestris var. mongolica. We recommend to randomly select three sample trees per plot measuring tree heights for parameters estimation of mixed models, and calculating random parameters.