ObjectiveBased on the data of 5211 sample trees in 61 permanent sample plots in Mongolian pine plantations from Maoershan Experimental Forest Farm, Hengtoushan Forest Farm, Mengjiagang Forest Farm in Heilongjiang Province of northeastern China, the simultaneous equations for tree height model and height to crown base model were developed.

MethodAt first, 2 alternative height-diameter models had been selected by comparing the goodness of fit for 8 height-diameter models. From 5 basic height to crown base(HCB)models, 3 best HCB models including tree and stand variables (tree size, competition index, site condition) were selected as alternative models using the method of all subset regression. Based on the seeming unrelated regression (SUR), the parameters of the simultaneous equations model of height and HCB were estimated considering each kind of combinations for 2 alternative height-diameter models and 3 alternative HCB models, respectively. Finally, we evaluated the fitting effect of the simultaneous equation model.

ResultThe results showed that H and HCB were positively correlated with basal area (G) and average height of dominant tree (H₀). For the best simultaneous equations, the coefficient determination (R_a²) was 0.9520 and the root-mean-square error (RMSE) was 1.17m by fitting height (H), the R_a² was 0.9066, and RMSE was 1.36m by fitting HCB. The validation values of the best simultaneous equations were smaller.

ConclusionOn the whole, the simultaneous equations developed performed well in predicting the tree H and HCB simultaneously with the least predicting errors, and the model could handle correlations between tree H and HCB. The simultaneous equations considering stand variables developed in this paper could be suitable for predicting H and HCB for Mongolian pine plantations with different stand conditions and it will provide basis for future research on the crown structure and dynamics.