基于分位数回归及混合模型的针叶树树冠轮廓及结构因子模拟

This study regards three conifer species Larch (Larix spp.), Korean pine (Pinus koraiensis.), and Mongolian pine (Pinus sylvestnis.) in the plantations of the Northeast, P.R. China as the research object. Based on stem analysis data, branch analysis data and crown biomass data of long-term observation, and a lot of remeasured data from permanent sample plot in which the database consists stand variables, tree size variables and branch attributes variables, the static and dynamic development of crown structure for different stand conditions (i.e., stand age and stand density) and tree sizes are analyzed. The new theory and method of modern statistics (i.e., segmented regression, quantile regression, multi-level linear or nonlinear mixed effects models joint distribution models, and simultaneous equations model) will be adopted in this research. A new modeling approach based on the quantile regression for nonlinear mixed-effects models proposed by this study is used to develop the crown profile models. The static models of branch and crown attributes, and branch growth and branch mortality probability models are developed by combining distribution functions and the theoretical growth functions of tree with multi-level mixed effects models with parameter random effect of stand, tree and branch simultaneous, and the dynamic of branch, crown and canopy are quantitatively simulated. According to the relationship between the foliage vertical distribution and stem diameter increment, the effective crown is determined and the model of height to effective crown from ground is developed. Therefore, without impacting tree growth, the height of manual pruning and intensity of thinning for different stand conditions will be reasonably determined for improving the quality and value of the wood. This research will provide scientific basis for comprehensively improving plantation productivity and the stand stocking volume per hectare.

本研究以东北地区落叶松，红松和樟子松人工林为研究对象，基于长期调查收集的树干解析、枝条解析、树冠生物量数据，结合固定样地复测数据（包括林分、林木、枝条变量），分析不同林分条件（年龄和林分密度）下不同大小林木的树冠结构因子静态和动态发育规律；组合近代统计学新理论和新方法（如分段函数回归、分位数回归、多个水平线性与非线性混合模型、联合分布模型、联立方程组模型等），提出非线性混合模型结合分位数回归构建树冠轮廓模型的新方法；采用分布函数和理论生长方程与多水平（林分—林木—枝条）混合模型相结合方法，建立枝条和树冠特征因子静态模型及枝条生长和枯损模型，定量模拟枝条、树冠及冠层动态；根据叶量垂直分布与树干生长关系确定有效树冠，构建有效冠高的预测模型，从而在不影响林木生长前提下，合理确定不同林分条件下人工整枝高度以及抚育间伐强度，提高木材质量和价值，为全面提高人工林生产力和林分质量提供科学依据。

红松（Pinus koraiensis）、长白落叶松（Larix olgensis）、樟子松（Pinus sylvestris var. mongolica）是东北重要的针叶造林树种，对其树冠结构的模拟为研究生物量、竞争、林分动态生长等提供理论基础，为制定合理的经营决策提供科学依据。本研究基于固定样地、解析木和枝解析数据，利用分位数回归、联立方程组、混合效应模型等方法，构建了一套涵盖了树冠轮廓、树冠和枝条特征因子、树冠动态模拟的模型系统。本研究结果表明：利用非线性分位数回归模型分别模拟了三个树种的外部轮廓曲线和最大外部轮廓曲线。在q=0.90处的树冠轮廓曲线的拐点能够较好预测的最大树冠半径。落叶松内部轮廓是一条起始于梢头下某一位置，终止于树冠基部的直线。通过树冠最大外部轮廓曲线积分获得树冠体积和表面积，构建了树冠体积、表面积通用模型，模型具有较高精度。结合枝条净碳贡献量、树干断面积生长量与叶量垂直分布，最终将累积叶量达到90%时的高度确定为有效冠高。采用Weibull分布模拟树冠内叶面积的垂直分布，计算不同林分条件、不同大小解析木的有效冠高，建立了有效冠高预估模型。一级、二级枝条数量分布模型结果表明一级枝条和二级枝条数量在树冠内呈现增大后减小的趋势。基于分位数线性混合效应模型模拟了三个树种最大基径模型和潜在最大基径模型。构建的枝条相对基径模型、枝条长度和角度模型、枝条存活概率模型（个体水平和轮层水平）均具有较好的模拟效果。结合以上枝条特征因子模型，可以很好的描述枝条在树冠垂直方向和水平方向的变化。根据建立的枝条基径生长、枝长生长和枝下高动态预估模型，可以很好地从水平和垂直方向模拟树冠动态生长。