Crown-shape model of a Pinus koraiensis plantation in northeastern China

Using the data of 4 538 branches from 79 Pinus koraiensis in Mengjiagang forest farm of Heilongjiang Province, northeastern China, we deduced continuous segmented function with biological constraints of tree crown profile (crown width at top of tree is 0 and the maximum value at inflection point) based on the segmented regression of spline function theory, and developed the crown profile models (i.e. segmented parabola equation,segmented Mitscherlich equation and segmented power equation) for Pinus koraiensis. The goodness-of-fitting index,validation results of the models and the reasonability from estimating the inflection points were used to evaluate all models and select the optimal model for predicting crown profile of Pinus koraiensis. With the re-parameterization of the model parameters and the analysis of the correlation between the parameters and tree variables, diameter at the breast height (DBH) was introduced into the optimal model, and the crown-shape predicting model for Pinus koraiensis was established. The results showed that the segmented parabola function was the optimal equation to describe crown profile for Pinus koraiensis. The crown size and parameters of the crown profile were positively correlated with DBH. For the crown-shape predicting model after re-parameterization, the coefficient of determination (R2a) was 0.659 6, the standard error (Sy.x) of estimation was 0.524 5 and the mean square error (MSE) was 0.227 9. Meanwhile, the prediction precision (p) was 97.58%. With the increase of DBH, the range of inflection point of Pinus koraiensis crown profile (relative crown depth) is between 0.72-0.95 with a mean value of 0.81. On the whole, the crow-shape predicting model with DBH as independent variable and the tree top as constraint performed well in predicting the crown profile for Pinus koraiensis, which provides basis for estimating crown structure of Pinus koraiensis in plantations.