Taper functions to predict the upper stem diameter of Chir pine (Pinus roxburghii) in the mid-hills of Nepal

Abstract

A function that predicts the upper stem diameters of an individual tree is helpful in better quantifying the volume and devising sustainable management of commercially and ecologically important species. This study compares three forms of the taper equation (single, variable-exponent, and segmented) using destructive sample data collected from 80 Chir pine (Pinus roxburghii Sarg.) trees across three adjacent stands in the Mid hills of Nepal. A mixed-effects modeling approach was used to evaluate the 13 different taper functions, selecting the best parameter association with the random effect to avoid overparameterization. Additionally, these models were fitted to minimize errors by modeling correlation structure with continuous autoregressive correlation structure of order 1 (corCAR1) and variance with a power variance function. All models were statistically significant at 5% level in the likelihood ratio test when compared with the models fitted without these error minimization. Furthermore, model performance (root mean square error, mean absolute error, and pseudo-R2) was evaluated using k-fold cross-validation procedure. Although all taper functions described more than 95% of the variation in upper stem diameter prediction, the single-form models of Bennett and Swindel (1972) and Amidon (1984), the variable-exponent model form of Sharma and Zhang (2004), and the segmented model form of Max and Burkhart (1976) explained more than 98% percent of the variability. Residual diagnostics indicated that Sharma and Zhang's (2004) model provided better constant and minimum errors in predicting the upper stem diameter along the 8 to 20 m stem length, whereas other models exhibited higher residual errors. Despite model's better performance, variability along the upper stem diameter prediction would affect its applicability in estimating the volume at any merchantable height of individual trees.

Keywords

• Maximum likelihood
• Mixed-effects model
• Autocorrelated errors
• Variance function matrix
• K-fold cross-validation