應用增幅式迴歸樹方法建立臺灣杉直徑分布模型

Abstract

本研究目的是建立經過疏伐經營後的臺灣杉直徑分布模型。我們使用兩處由 林業試驗所設置的臺灣杉(Taiwania cryptomerioides)試驗林來建立模型。這兩 處試驗林分別位於臺灣南部的六龜與藤枝地區，氣候以及環境條件相似。六龜試 驗林是由三十六個樣區所組成的兩公頃林分，而藤枝試驗林則是二十四個樣區所 組成的 1.6 公頃林分。首先，我們將比較四個機率分布模型(Probability density functions)對於臺灣杉直徑分布的適合度(Goodness of fit)。在這四個模型中，三 參數韋伯分布(Three-parameters Weibull function)為最適合模型。再來，我們將 林分因子分為疏伐前與疏伐後兩組來預測韋伯分布的三個參數。為了選出具有影 響力的林分因子，本研究使用機器學習領域中的增幅式迴歸樹(Boosted Regression Tree)來做變數的選擇。根據迴歸樹結果，擁有較高相對貢獻度 (Relative Contribution)的林份因子會被留下並且利用彷彿無相關迴歸 (Seemingly Unrelated Regression)建立韋伯參數與林份因子的線性模型。根據結 果，直徑分布的偏度和峰度在疏伐前與形狀參數呈負相關，而距離疏伐的年份與 尺度因子呈正相關，平方平均直徑則與位置參數呈正相關。在疏伐後，直徑分布 的偏度影響了所有的韋伯參數，而距離疏伐的年份與平方平均直徑則持續分別與 尺度因子和位置因子呈正相關。

The purpose of this study is to predict future stand diameter distribution for Taiwania cryptomerioides plantations under different thinning intensity. We used data from two experimental forests established by the Taiwan Forest Research Institute (TFRI), which are Liouguei Experimental Forests and Tengjhih Experimental Forests. Areas of the two study sites are 2 and 1.44 ha, and they are divided into 36 and 24 plots, respectively. Elevation of both sites is about 1400 m a.s.l., and the weather conditions are similar between these two sites. Firstly, we would compare goodness of fit of four probability density functions(PDF). The parameters of PDFs describing diameter distribution were estimated by the method of maximum likelihood. The best PDF for fitting diameter distribution of our data was three-parameters Weibull function (3Weibull). Afterwards, we modelled the estimated 3Weibull parameters as the responses of stand condition predictors. Two sets of stand conditions were prepared, one before thinning and another after thinning so that two regression models were built for the estimated Weibull parameters. To identify stand condition predictors in the two sets that are significant, we apply Boosted Regression Tree (BRT) as the method of variable selection, which is a statistical learning method with accurate prediction. For each set of predictors, stand condition predictors that had high relative contributions are retained. These predictors were used to build linear models for each estimated 3Weibull iv parameters with Seemingly Unrelated Regression (SUR). The linear models showed that influential predictors and directional effects differed across two predictors sets and 3Weibull parameter. In before thinning models, the skewness and the kurtosis of diameter distribution most affected the shape parameter, and both associated negatively with it. Years after thinning significantly increased the scale parameter, and the quadratic mean diameter positively influenced the location parameter. In after thinning models, all 3Weibull parameters were strongly linked to the skewness of diameter distribution. Years after thinning and the quadratic mean diameter still significantly affected and positively associated with the scale and the location parameter, respectively.