Predicting height to crown base for Larix gmelinii using quantile groups

  Objective  Quantile regression and quantile groups were used in this article to model and predict height to crown base, which provided new ideas and methods for the construction of height to crown base models.

  Method  The data were collected from the measured data of natural forests of Larix gmelinii in 4 forest farms of Xinlin in Daxing’ anling of northeastern China. Nonlinear regression was used to build the basic and generalized models of the height to crown base and then extended to quantile regression. Four types of sampling designs (the largest DBH tree sampling, the smallest DBH tree sampling, the mean DBH tree sampling and random sampling) and three quantile group ($\tau {\text{ = }}$ 0.1, 0.5, 0.9), five quantile group ($\tau {\text{ = }}$ 0.1, 0.3, 0.5, 0.7, 0.9), nine quantile group ($\tau {\text{ = }}$ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) were used to predict height to crown base. The prediction effects of different quantile groups were compared as well as the impact of different sampling designs. Two-fold evaluation was used to compare the prediction effects of nonlinear regression, optimal quantile regression and optimal quantile group. Model evaluation criteria included mean absolute error (MAE), root mean square error (RMSE), mean percentage of error (MPE) and adjustment determination coefficient (${{R}}_{{\rm{adj}}}^2$).

  Result  (1)Whether it is nonlinear regression or quantile regression, the fitting MAE of generalized models can be reduced by 6% to 12%, RMSE can be reduced by 6% to 10% compared with basic models. And the validation effects of generalized models were also better than basic models. There was a negative correlation between height to crown base and DBH, and a positive correlation between height to crown base and H_DOM and BA. (2) Median regression had the best fitting ability among all quantiles, and the effects of median regression were similar to that of nonlinear regression. Quantile regression can describe the distribution of height to crown base. (3) All three quantile groups can predict height to crown base and the effect was not much different. The three quantile group was sufficient to predict height to crown base. The results of two-fold evaluation for median regression were similar to that of nonlinear regression, while three quantile group’s prediction ability was the best. Compared with nonlinear regression and median regression, the MAE and MPE of three quantile group decreased about 20% and 4% respectively, ${{R}}_{{\rm{adj}}}^2$ increased about 16%. (4) The optimal sampling designs for basic and generalized quantile groups were five mean DBH trees and seven largest trees, respectively.

  Conclusion  The height to crown base models based on three quantile group ($\tau {\text{ = }}$ 0.1, 0.5, 0.9) in this study can improve the prediction accuracy. The optimal sampling design of the basic and generalized quantile groups is 5 mean DBH tree sampling and 7 largest DBH tree sampling, respectively. Considering the accuracy of prediction and the cost of investigation, it is recommended to select 5 medium trees from the sample plot to predict the height to crown base when quantile groups are applied in practice.