Abstract:

【Objective】 The aim of this study was to develop a stem taper equation based on the quantile regression method for Larix gmelinii in Greater Khingan Mountains. We compared and analyzed the prediction precision of basic models, different quantile (τ=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) models, and quantile group models using different upper-stem diameters. These studies provide a theoretical basis for the precise prediction of the natural forest taper of L. gmelinii. 【Method】 The stem taper data of 212 L. gmelinii in Greater Khingan Mountains, Songling Forest Bureau, were the research object. Based on the nonlinear quantile regression method and Max and Burkhart segmented taper equation, the nonlinear programming (NLP) method in SAS software was used to fit the stem taper equation of different quantiles. Calibration of the taper equations was carried out using the upper-stem diameter measured at the relative heights of 20%, 30%, 40%, 50%, 60%, 70%, and the midpoint between the breast height and the tip of the tree (50%^*). The mean absolute bias (MAB) and mean percentage of bias (MPB) were used as statistical criteria to compare the calibrated stem taper equations. 【Result】 The parameters of the Max and Burkhart segmented taper equations based on nine different quantiles were obtained, allowing the prediction ability of the quantile regression taper model in different quantiles to be evaluated. The prediction accuracy of the uncalibrated quantile models at the quantile (τ=0.5, 0.6) was slightly better than the uncalibrated basic model. Accurate choices of the localized position were essential. Compared with the uncalibrated basic model, the prediction accuracy of each quantile group model for the calibrated stem taper using the upper-stem diameter measured at relative heights of 20% and 70% was not improved. The prediction accuracy of the most quantile group (3, 5, 7, 9) models calibrated using the upper stem measurements at relative heights of 30%, 40%, 50%, 60% and the midpoint between the breast height and the tip of the tree was improved. The overall prediction accuracy using a quantile group model for the calibrated positions was 40%>50%^*>50%>60%>30%>20%>70%. The best calibration position was the relative height of 40% of the tree, and the three quantile (τ=0.3, 0.5, 0.7) group model had the highest prediction accuracy. Both MAB and MPB decreased by 13.5% compared to the uncalibrated basic model. 【Conclusion】 Introducing a reasonable calibration position in the taper equation improved the prediction accuracy of the models. The best calibration position was the relative height of 40% of the tree with the group of three quantiles (τ =0.3, 0.5, 0.7). In practical applications, if the calibration is not considered, it is recommended that the quantile (τ =0.5) should be used.

Key words: Larix gmelinii, combined quantile, calibration position, taper equation, prediction precision