大兴安岭地区天然落叶松—白桦混交林分树种直径分布研究
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摘要
本文以大兴安岭地区109块落叶松-白桦天然混交林为研究对象,对混交林分树种直径分布进行研究,即在已知总的林分直径分布信息的基础上,得出每个组成树种的直径分布信息。研究的109块落叶松-白桦天然混交林样地都通过了Weibull分布的检验,因此,选择Weibull分布函数作为基础模型。采用三种方法进行研究,有限混合分布模型(finite mixture models简称FMM)法、联立方程组法和矩解法参数回收系统,与传统的方法比较。本文主要贡献和研究结果如下：
(1)有限混合分布模型(FMM)法,利用以Weibull分布函数为混合成分的有限混合分布模型(FMM),对混交林分树种直径分布进行研究,并与传统的方法进行比较(在不分树种情况下,用单独的Weibull分布函数对全林分的直径分布拟合；分树种,即对落叶松和白桦分别拟合Weibull分布函数直径分布模型,整个样地的各径阶的株数由求得的落叶松和白桦的各径阶加和得到)。研究结果表明：
a)有限混合分布模型利用了整个样地的径阶频数分布信息,充分的考虑了两个组成树种在整个样地中的相互关系,可得出两个组成树种的直径分布,并给出了两个组成树种的比例信息。但是,对各组成树种(落叶松和白桦)的比例的估计效果不是很理想,对每个树种组成的直径分布的模拟精度不高。但是对整个样地的直径分布的模拟效果相当好,无论是单峰曲线还是双峰曲线,反J型还是M型,都体现了非常灵活的拟合效果。
b)传统方法对各组成树种(落叶松和白桦)的直径分布的模拟和比例的估计好于有限混合分布模型(FMM)法,但是对整个样地的模拟逊于有限混合分布模型(FMM)法。并且传统方法对规则的曲线形式特别是规则的反J型拟合效果好,对具有单峰的或双峰的分布形式拟合不好。
(2)联立方程组法,利用林分中林木直径的简单统计量—算术平均直径(D)、平均直径(Dg)、直径标准差(SD)、变异系数(CV)、偏度(skewness)、峰度(kurtosis)、直径最小值(Dmin)和直径最大值(Dmax)这些信息,建立了大兴安岭地区天然落叶松-白桦混交林分树种直径分布联立方程组模型。实现了在获得这些简单统计量的前提下,求得全林分和分树种组成的直径分布Weibull函数的尺度参数和形状参数。研究结果表明：
a)建立的大兴安岭地区天然落叶松-白桦混交林分树种直径分布联立方程组模型,无论是对整个样地直径分布的模拟还是分树种直径分布的拟合都取得了比理想的效果。
b)并与有限混合分布模型(FMM)和传统的模型比较,结果发现,对于整个样地的直径分布的模拟稍逊于有限混合分布模型(FMM),优于传统的模型；对于分树种组成落叶松和白桦的直径分布的模拟优于有限混合分布模型(FMM)和传统的方法。对于组成树种的比例的估计偏差较小,明显优于有限混合分布模型(FMM)。但对于落叶松和白桦的直径的均值和方差的差异比较小时,估计的比例会出现很大的偏差,这是此方法的不足之处。
(3)建立大兴安岭地区天然落叶松-白桦混交林分树种直径分布Weibull函数参数的矩解法回收系统。这个系统包含两个部分,一是利用全林分的直径分布信息及林分因子(算术平均直径D、平均直径Dg、最小直径Dmin、0.06公顷上林木株数N、林分年龄t和林分平均高H),建立落叶松—白桦算术平均直径(LD和BD)和平均直径(LD8和BDg)的模型,二是利用落叶松—白桦算术平均直径(LD和BD)和平均直径(LDg和BDg),用矩解法回收(求解)出落叶松和白桦的直径Weibull分布函数的参数。实现,由全林分的直径分布信息及林分因子(算术平均直径D、林分平均Dg、最小直径Dmin、0.06公顷上林木株数N、林分年龄t和林分平均高H),利用矩解法分别回收(求解)出落叶松-白桦的直径Weibull分布函数的参数,为以后研究林分直径动态变化,提供研究基础。研究结果表明：
a)本文建立的大兴安岭地区天然落叶松-白桦混交林分树种直径分布Weibull函数的参数的矩解法回收系统,对整个林分的直径模拟和对每个树种的直径分布模拟,都取得了理想的效果,可以用于对林分分树种收获量预估的研究。
b)与FMM方法和传统的方法比较,对整个样地的拟合逊于FMM方法,优于传统的方法；对于每个树种的模拟优于FMM方法和传统的方法。但效果稍逊于上面建立的联立方程组法。
综合以上得出,有限混合分布模型(FMM)法对于解决混交林分树种直径分布的拟合没有达到预期的效果,但是可以用有限混合分布模型(FMM)拟合不规则多峰的林分直径分布曲线形式。混交林分树种直径分布联立方程组模型达到了本文的研究目的,可以用于对天然落叶松-白桦混交林分树种直径分布的模拟。三种方法比较,有限混合分布模型(FMM)对分树种直径分布的拟合效果不理想,但对整个样地的直径分布拟合效果很好；联立方程组法和矩解法参数回收系统对分树种的直径分布和整个样地的直径分布的拟合效果理想,均达到了本文的研究目的,效果都好于传统的对分树种单独拟合直径分布的方法,矩解法参数回收系统也可以用于下一步对林分收获量的预估和林分直径结构的动态研究。
对混交林分树种直径分布进行研究具有很大的实际意义,获得整个样地的直径分布信息的同时又能得到分树种的直径分布信息,可以实现对全林分的最优化经营条件下还可以分树种进行经营和管理,获得最优的经营管理措施组合,对更加细化的林业经营管理具有参考价值。
The purpose of this study is to disaggregate diameter distribution of mixed forest, namely when the information of the whole stand diameter distribution is known, the diameter distribution of each individual specie component can be obtained. The paper select109sample plots as the study object to disaggregate diameter distribution of mixed forest. In this paper, three methods are used:a finite mixture model (FMM); a simultaneous equations model; the system of moments for diameter distribution parameter recovery.
(1) A finite mixture model (FMM) is used to disaggregate diameter distribution of mixed forest, comparing with traditional methods including a single Weibull function to fit the whole plot only and a single Weibull function to fit each species component separately and the summation of the individual species produced the whole plot.
a) FMM fits the species component distributions simultaneously with the constraint that the individual components add up to the whole plot, without requiring the observed frequencies for each species across the diameter classes, as well as provide the distribution estimation for each species component and the mixing proportions. But the distribution estimation for each species component and the mixing proportions are not ideal.
b) Traditional methods are only suitable to regular and unimodal diameter distributions such as balanced reversed-J shape. Although Traditional methods may be able to fit each species component well if its frequency distribution is known and available in the data, they ignore the inter-species relationships within a given plot. Thus, the summation of the species components may not produce a good fit for the whole plot.
c) The FMM models are more flexible to describe highly skewed and irregular diameter distributions for the whole plot.
(2) A simultaneous equations model is used to disaggregate diameter distribution of mixed forest, the method applies mainly simple statistics of diameter-the arithmetic mean diameter of stand (DBH), the mean diameter of stand(Dg), the standard deviations of diameter(SD), the coefficient of variation of diameter(CV), skewness, kurtosis, the minimum diameter(Dmin), the maximum diameter(Dmax) to disaggregate diameter distribution of each species component.
a) The simultaneous equations model can obtain scale parameter b and shape parameter c for diameter Weibull distribution of each species component in natural mixed forest of Larix gmelini and Betula platyphylla in Hei longjiang. The results show the simultaneous equations model for diameter Weibull distribution of each species component in natural mixed forest of Larix gmelini and Betula platyphylla in Hei longjiang yielded promising results, whether if each species component or the whole stand.
b) Comparing with traditional methods, a simultaneous equations model takes on better effects. Because the method can characterizes either unimodal diameter distributions or highly skewed and irregular diameter distributions.
3A system of moments for diameter distribution parameter recovery is used to disaggregate diameter distribution of mixed forest. The method used the stand factors, including the arithmetic mean diameter of plot (DBH), the mean diameter of plot (Dg), the minimum diameter (Dmin), the stand age(t) and the stand mean height (H), to develop the system of moments for diameter distribution parameter recovery. The system include two steps, the first is to use these factors to model the arithmetic mean diameter of Larix and white birch (LD and BD) and the mean diameter of Larix and white birch (LDg and BDg), the second is to used LD, BD, LDg and BDg to recovery parameters of diameter distribution of Larix and white birch. The results show:
a) The method can characterizes diameter distribution of each species of mixed forest. This system can also be used to study on estimating each species yields by size class.
b) Comparing FMM, traditional methods and simultaneous equations model, this system characterizes the whole stand better than traditional methods; for characterizing each species, underperforming simultaneous equations model and better than FMM, traditional methods.
The study to disaggregate diameter distribution of mixed forest can provide foundation for more refined and effective forest management and planning.
(1)有限混合分布模型(FMM)法,利用以Weibull分布函数为混合成分的有限混合分布模型(FMM),对混交林分树种直径分布进行研究,并与传统的方法进行比较(在不分树种情况下,用单独的Weibull分布函数对全林分的直径分布拟合；分树种,即对落叶松和白桦分别拟合Weibull分布函数直径分布模型,整个样地的各径阶的株数由求得的落叶松和白桦的各径阶加和得到)。研究结果表明：
a)有限混合分布模型利用了整个样地的径阶频数分布信息,充分的考虑了两个组成树种在整个样地中的相互关系,可得出两个组成树种的直径分布,并给出了两个组成树种的比例信息。但是,对各组成树种(落叶松和白桦)的比例的估计效果不是很理想,对每个树种组成的直径分布的模拟精度不高。但是对整个样地的直径分布的模拟效果相当好,无论是单峰曲线还是双峰曲线,反J型还是M型,都体现了非常灵活的拟合效果。
b)传统方法对各组成树种(落叶松和白桦)的直径分布的模拟和比例的估计好于有限混合分布模型(FMM)法,但是对整个样地的模拟逊于有限混合分布模型(FMM)法。并且传统方法对规则的曲线形式特别是规则的反J型拟合效果好,对具有单峰的或双峰的分布形式拟合不好。
(2)联立方程组法,利用林分中林木直径的简单统计量—算术平均直径(D)、平均直径(Dg)、直径标准差(SD)、变异系数(CV)、偏度(skewness)、峰度(kurtosis)、直径最小值(Dmin)和直径最大值(Dmax)这些信息,建立了大兴安岭地区天然落叶松-白桦混交林分树种直径分布联立方程组模型。实现了在获得这些简单统计量的前提下,求得全林分和分树种组成的直径分布Weibull函数的尺度参数和形状参数。研究结果表明：
a)建立的大兴安岭地区天然落叶松-白桦混交林分树种直径分布联立方程组模型,无论是对整个样地直径分布的模拟还是分树种直径分布的拟合都取得了比理想的效果。
b)并与有限混合分布模型(FMM)和传统的模型比较,结果发现,对于整个样地的直径分布的模拟稍逊于有限混合分布模型(FMM),优于传统的模型；对于分树种组成落叶松和白桦的直径分布的模拟优于有限混合分布模型(FMM)和传统的方法。对于组成树种的比例的估计偏差较小,明显优于有限混合分布模型(FMM)。但对于落叶松和白桦的直径的均值和方差的差异比较小时,估计的比例会出现很大的偏差,这是此方法的不足之处。
(3)建立大兴安岭地区天然落叶松-白桦混交林分树种直径分布Weibull函数参数的矩解法回收系统。这个系统包含两个部分,一是利用全林分的直径分布信息及林分因子(算术平均直径D、平均直径Dg、最小直径Dmin、0.06公顷上林木株数N、林分年龄t和林分平均高H),建立落叶松—白桦算术平均直径(LD和BD)和平均直径(LD8和BDg)的模型,二是利用落叶松—白桦算术平均直径(LD和BD)和平均直径(LDg和BDg),用矩解法回收(求解)出落叶松和白桦的直径Weibull分布函数的参数。实现,由全林分的直径分布信息及林分因子(算术平均直径D、林分平均Dg、最小直径Dmin、0.06公顷上林木株数N、林分年龄t和林分平均高H),利用矩解法分别回收(求解)出落叶松-白桦的直径Weibull分布函数的参数,为以后研究林分直径动态变化,提供研究基础。研究结果表明：
a)本文建立的大兴安岭地区天然落叶松-白桦混交林分树种直径分布Weibull函数的参数的矩解法回收系统,对整个林分的直径模拟和对每个树种的直径分布模拟,都取得了理想的效果,可以用于对林分分树种收获量预估的研究。
b)与FMM方法和传统的方法比较,对整个样地的拟合逊于FMM方法,优于传统的方法；对于每个树种的模拟优于FMM方法和传统的方法。但效果稍逊于上面建立的联立方程组法。
综合以上得出,有限混合分布模型(FMM)法对于解决混交林分树种直径分布的拟合没有达到预期的效果,但是可以用有限混合分布模型(FMM)拟合不规则多峰的林分直径分布曲线形式。混交林分树种直径分布联立方程组模型达到了本文的研究目的,可以用于对天然落叶松-白桦混交林分树种直径分布的模拟。三种方法比较,有限混合分布模型(FMM)对分树种直径分布的拟合效果不理想,但对整个样地的直径分布拟合效果很好；联立方程组法和矩解法参数回收系统对分树种的直径分布和整个样地的直径分布的拟合效果理想,均达到了本文的研究目的,效果都好于传统的对分树种单独拟合直径分布的方法,矩解法参数回收系统也可以用于下一步对林分收获量的预估和林分直径结构的动态研究。
对混交林分树种直径分布进行研究具有很大的实际意义,获得整个样地的直径分布信息的同时又能得到分树种的直径分布信息,可以实现对全林分的最优化经营条件下还可以分树种进行经营和管理,获得最优的经营管理措施组合,对更加细化的林业经营管理具有参考价值。
The purpose of this study is to disaggregate diameter distribution of mixed forest, namely when the information of the whole stand diameter distribution is known, the diameter distribution of each individual specie component can be obtained. The paper select109sample plots as the study object to disaggregate diameter distribution of mixed forest. In this paper, three methods are used:a finite mixture model (FMM); a simultaneous equations model; the system of moments for diameter distribution parameter recovery.
(1) A finite mixture model (FMM) is used to disaggregate diameter distribution of mixed forest, comparing with traditional methods including a single Weibull function to fit the whole plot only and a single Weibull function to fit each species component separately and the summation of the individual species produced the whole plot.
a) FMM fits the species component distributions simultaneously with the constraint that the individual components add up to the whole plot, without requiring the observed frequencies for each species across the diameter classes, as well as provide the distribution estimation for each species component and the mixing proportions. But the distribution estimation for each species component and the mixing proportions are not ideal.
b) Traditional methods are only suitable to regular and unimodal diameter distributions such as balanced reversed-J shape. Although Traditional methods may be able to fit each species component well if its frequency distribution is known and available in the data, they ignore the inter-species relationships within a given plot. Thus, the summation of the species components may not produce a good fit for the whole plot.
c) The FMM models are more flexible to describe highly skewed and irregular diameter distributions for the whole plot.
(2) A simultaneous equations model is used to disaggregate diameter distribution of mixed forest, the method applies mainly simple statistics of diameter-the arithmetic mean diameter of stand (DBH), the mean diameter of stand(Dg), the standard deviations of diameter(SD), the coefficient of variation of diameter(CV), skewness, kurtosis, the minimum diameter(Dmin), the maximum diameter(Dmax) to disaggregate diameter distribution of each species component.
a) The simultaneous equations model can obtain scale parameter b and shape parameter c for diameter Weibull distribution of each species component in natural mixed forest of Larix gmelini and Betula platyphylla in Hei longjiang. The results show the simultaneous equations model for diameter Weibull distribution of each species component in natural mixed forest of Larix gmelini and Betula platyphylla in Hei longjiang yielded promising results, whether if each species component or the whole stand.
b) Comparing with traditional methods, a simultaneous equations model takes on better effects. Because the method can characterizes either unimodal diameter distributions or highly skewed and irregular diameter distributions.
3A system of moments for diameter distribution parameter recovery is used to disaggregate diameter distribution of mixed forest. The method used the stand factors, including the arithmetic mean diameter of plot (DBH), the mean diameter of plot (Dg), the minimum diameter (Dmin), the stand age(t) and the stand mean height (H), to develop the system of moments for diameter distribution parameter recovery. The system include two steps, the first is to use these factors to model the arithmetic mean diameter of Larix and white birch (LD and BD) and the mean diameter of Larix and white birch (LDg and BDg), the second is to used LD, BD, LDg and BDg to recovery parameters of diameter distribution of Larix and white birch. The results show:
a) The method can characterizes diameter distribution of each species of mixed forest. This system can also be used to study on estimating each species yields by size class.
b) Comparing FMM, traditional methods and simultaneous equations model, this system characterizes the whole stand better than traditional methods; for characterizing each species, underperforming simultaneous equations model and better than FMM, traditional methods.
The study to disaggregate diameter distribution of mixed forest can provide foundation for more refined and effective forest management and planning.
引文
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