Abstract:

【Objective】Based on the nonparametric theory, the nonparametric additive taper equation was constructed for dahurian larch (Larix gmelinii) in Greater Khingan Mountains. The common parametric taper equation of Max and Burkhart, in forestry, was used for comparison.【Method】A nonparametric additive taper equation was constructed using the total height, diameter at breast height, diameter at different heights, height at different stems, and their transformation. The nonparametric model was fitted based on the Gamm function in the mgcv library of the R software. Specifically, we used 7 smooth splines: thin plate regression splines (TP), Duchon splines (DS), cubic regression splines (CR), P-splines (PS), Gaussian process smooths (GP), B-spline (BS), and local regression (LO).【Result】The optimal nonparametric form of taper equation was constructed using response variable relative diameter (d/D) and explanatory variables such as the square of diameter at breast height (D²), total height (H) and square root of relative height($\sqrt{h/H}$). Fitting results showed that the additive taper equations based on CR and LO had smaller R² and larger AIC values, and the residual trend lines of CR and LO were slightly higher in the middle and lower at both ends. The nonparametric additive taper equation fitting effects of the other 5 smooth splines were similar. The fitting results of these additive models are better than those of Max and Burkhart, except for LO model. The overall validation results showed that the nonparametric models (TP, DS, PS, GP and BS) were basically consistent with the fitting results, except for CR. That is, they were superior to the parametric taper equation of Max and Burkhart. The error comparison based on the prediction of different height diameters of stems showed that the average error and absolute mean error of the nonparametric models (TP, DS, PS, GP and BS) were less than those of Max and Burkhart at most heights, except for CR. 【Conclusion】The nonparametric models (TP, DS, PS, GP and BS) showed consistent accuracy in fitting statistics, residual distribution, and the prediction from overall and different heights. These models are superior compared to those commonly used parametric taper equation of Max and Burkhart in forestry. When prediction is the main purpose for building a model, the nonparametric additive taper equation constructed in this study can be used not only to predict the shape of the stem but also the volume of the dahurian larch in Daxing’anling.

Key words: nonparametric models, spline function, taper equation, Larix gmelinii