北京地区油松林分生长、枯损和进界模型的研究
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摘要
森林是陆地生态系统的主体，是维持生态平衡和改善生态环境的重要保障，在应对全球气候变化中发挥着不可替代的作用。因此及时、准确、有效地监测和评价森林，对科学合理经营森林、充分发挥森林的多功能效益至关重要。森林资源的监测和评价的核心问题就是要及时了解森林生长、枯损和进界的动态变化情况。而及时了解森林生长、枯损和进界的动态变化，就必须应用森林模型技术。林分动态变化模型包括了生长、枯损和进界模型。应用林分动态变化模型可以使我们更深入地了解森林动态发展的模式，为有效地进行森林资源监测和合理地经营森林提供理论基础和分析评价方法。本研究以北京地区油松（Pinus tabulaeformis Carr.）林分为研究对象，根据林学和生物学特性，采用近代生物数学模型和统计分析方法，构建油松林分生长、枯损和进界动态变化模型：
（1）分别利用传统的固定生长率法和可变生长率法建立了单木直径年生长预测模型，并对这两种方法进行比较研究。研究结果表明，利用可变生长率法建立单木直径年生长预测模型，其均方根误差（RMSE=1.0182）比固定生长率法（RMSE=1.1393）的小，决定系数（R2=0.9310）比固定生长率法（R2=0.9136）的大，因此其拟合效果比固定生长率法好。可变生长率法估计单木生长模型参数时，考虑了林木因子的变化及通过建立林分模型预估林分变量因子（林分断面积，优势高）的变化，从而导致单木直径年生长量的变化，这符合林木生长的规律。同时，本研究也利用了可变生长率法建立了全林分年生长预测模型，该方法能够提供林分的年生长变化情况，并利用似乎不相关联立估计全林分生长模型参数，这样能够提高参数估计的有效性和一致性，减少系统估计误差。
（2）组合预测方法在提高模型预测精度方面有很好的表现。该方法充分利用单项预测模型所提供的有效信息，减少单个模型中随机因素的影响，把不同的模型误差分散化，从而提高预测精度。研究结果表明，组合预测模型精度（R2=0.9298）比单木模型（R2=0.9255）、林分模型（R2=0.9282）、分布模型（R2=0.9244）的预测精度都要高。利用组合预测估计方法预测林分断面积，使三个不同水平模型所得的林分断面积组合成一个预测值，保证了林分断面积预测的一致性，解决了不同预测模型间的相容性问题，为林分断面积生长模型一体化的研究提供了可行性。在组合预测模型中，权重的选取对提高组合预测结果的精度至关重要。相对于本研究所利用的误差平方和法和方差协方差法，最优加权法能够去除单项预测在组合预测模型中有偏的影响，从而使得组合预测达到无偏，最终达到提高预测精度的目的。
（3）解聚法以单木水平模型所得的林分变量尽可能地与林分水平模型所得的林分变量相匹配为迭代目标，进而调整单木生长模型以提高预测精度。本研究利用3种不同的解聚法（指数法，比例调整法，可加法）进行调整油松单木枯损，研究结果表明：这3种方法都提高了单木枯损的预测精度，可加法相对好于其它2种方法。相对于这2种迭代求解调整系数的方法，可加法直接通过调整系数公式计算得到，计算更加简单、有效。同时，在研究中我们也发现林分密度模型预测的精度在解聚法中起到重要的作用。林分株数密度预测精度高，那么就可以减少不同单木枯损预测方法的差别。组合预测法综合利用了不同水平模型所提供的信息，分散预测误差，进而提高林分变量预测精度。本研究中，我们结合解聚法和组合预测法调整单木枯损模型，研究结果表明综合利用这两种方法调整单木枯损，着实提高了单木枯损的预测精度。
（4）林分枯损和进界是描述林分动态变化特征的重要因子。然而，调查间隔期内可能有大量的样地没有发生林分枯损或进界现象，这意味着在所研究的数据中包含有大量的零数据，即数据结构是离散的。如果继续用最小二乘方法分析，估计不准确，会产生较大的偏差。本研究以计数类模型为基础，分别利用Poisson回归模型、负二项模型、零膨胀模型和Hurdle模型拟合林木枯损株数和林木进界株数，并通过AIC值，Pearson残差图以及Vuong检验对这些模型进行了详细分析比较。研究结果表明：Poisson回归模型不适用于模拟林木枯损株数。负二项回归模型相对于Poisson回归模型，比较适用。但是对于零枯损过多的数据，这两类模型拟合效果较差。零膨胀模型和Hurdle模型对这类数据有很好的解决办法。其中，零膨胀负二项模型和Hurdle-负二项模型拟合效果优于其它几种模型，而且这两个预测模型表现相当。本研究得出的结果可为分析林分枯损或者进界提供了一种可行性方法。
最后，利用C#.NET设置界面，通过SAS的IOM编程接口，实现了油松林分生长、枯损和进界动态变模型的系统集成。
The forest is the main body of terrestrial ecosystem. It plays a very crucial role inmaintaining ecological balance, improving ecological environment, as well as regulating globalclimate change. It is very important to forecast and evaluate forest resource accurately in timefor managing forest reasonably. The key problem of monitoring forest is how to know thedynamic change of foret growth, mortality and recruitment. As we know, the modelingtechnique is the basic method for knowing the forest dynamic change. Based on the forestdynamic models, we can know fully the forest development mode, which is helpful to monitorforest effectively and mange forest in reason. The dynamic models are composed of forestgrowth model, mortality model and recruitment model. In this study, based on the permanentdata of Chinese pine (Pinus tabulaeformis Carrière), the forest dynamic models includinggrowth, mortality and recruitment were developed using the modern biomathematics modeland statistical analysis method:
(1) The annual individual tree diameter model was developed with constant rate methodand variable rate method. Results showed that the variable rate method (RMSE=1.0182,R2=0.9310) outperformed the constant rate method (RMSE=1.1393, R2=0.9136) in predictingfuture individual tree diameter growth because the former accounted for the variable rate ofannual diameter growth, which was caused by changes of stand (basal area, dominant height)and tree attributes. It reflects the fact of tree growth. Also the whole stand models wereestablished with the variable rate method, which provided the annual forest stand changes. Theparameters of stand models were estimated via seemingly unrelated regression (SUR). Basedon the estimation method, the parameters had no obvious biases, and the precision of parameterestimation was more effectively.
(2) Forest combination method is a good method for improving model performance. Itefficiently uses information generated from different models to improve predictions byreducing errors from a single model. Results showed that the forecast combination method (R2=0.9298) provided overall better predictions of stand basal area than tree level model(R2=0.9255), stand level model (R2=0.9282) and distribution model (R2=0.9244). It alsoimproved the compatibility of stand basal area growth predicted from models of differentresolutions. In other words, it resolved the inconsistency of stand variable predictions atdifferent levels. It provided a method for integration of stand basal area. But we should alsorecognize that the method of calculating weights in combined models is very important. If themethod for calculating weights is good, then we will get the better results for combined model.In this thesis, the sum of squared errors method, variance-covariance method and optimalweight method were used to calculate the weights. The optimal weight method was superior toother two models, which removes the biased impact of single model on combined model, andthen gets the unbiased estimators.
(3) Disaggregation is a good method for improving prediction of tree models. In thismethod, individual-tree model predictions are adjusted so that the resulting sums would matchoutputs from a stand-level model. In this research, three disaggregation methods were used foradjusting tree mortality, which are power function method, proportional adjustment method,and addition method. Results showed that the disaggregation approach improved theperformance of tree survival models and the addition method performed slightly better than theother two disaggregation methods. An advantage of the addition method is that it alloweddirect computation of the adjusting coefficient, whereas the other methods required that theadjusting coefficient be resolved in an iterative manner. Meanwhile, we also showed thatstand-level prediction played a crucial role in refining outputs from a tree survival model,especially when it is a very simple model. Because the forecast combination method producedbetter stand-level prediction, we prefer the use of this method in conjunction with thedisaggregation approach, even though the performance gain in using the forecast combinationmethod shown for this data set was modest. And the results showed that the tree mortalityprediction was improved using the two methods together.
(4) Stand mortality and recruitment are very important variables for describing the standcharacters. Considering the fact that in permanent sample plots a relatively high number of the plots have no occurrences of recruitment or mortality even over periods of several years, itmeans that data are bounded and characteristically exhibit varying degrees of dispersion andskewness in relation to the mean. Additionally, the data often contain an excess number of zerocounts. Yet least squares method implicitly presumes that the data are Gaussian distributed withconstant variance, or at least satisfy the Gauss-Markov conditions. If the method is still used todeal with the data with large proportion of zero counts, the estimated results will be biased.Based on the theory of count models, poisson model, negative binomial model, zero-inflatedmodels and Hurdle models were used to analyze stand mortality and recruitment. The bestmodel was chose according to the AIC value, Pearson redidual plot and vuong test. Resultsshowed that: Poisson model was not suitable for stand mortality and recruitment, and negativebinomial was superior to the Poisson model. But both of them were not competent for theover-dispersion data. Zero-inflated model and hurdle model were fitted into the data.Additionally, zero-inflated negative binomial model (ZINB) and Hurdle-negative binomialmodel (HNB) outperformed than other models. The two models performed similarly inmodeling stand mortality and recruitment. The result provided a feasible method for analyzingstand mortality and recruitment.
Finally, integration system of forest growth, mortality and incruitment dynamic modelsfor Chinese pine was implemented. System interface was setup based on the C#. NET, linkedwith SAS through the SAS IOM programming.
（1）分别利用传统的固定生长率法和可变生长率法建立了单木直径年生长预测模型，并对这两种方法进行比较研究。研究结果表明，利用可变生长率法建立单木直径年生长预测模型，其均方根误差（RMSE=1.0182）比固定生长率法（RMSE=1.1393）的小，决定系数（R2=0.9310）比固定生长率法（R2=0.9136）的大，因此其拟合效果比固定生长率法好。可变生长率法估计单木生长模型参数时，考虑了林木因子的变化及通过建立林分模型预估林分变量因子（林分断面积，优势高）的变化，从而导致单木直径年生长量的变化，这符合林木生长的规律。同时，本研究也利用了可变生长率法建立了全林分年生长预测模型，该方法能够提供林分的年生长变化情况，并利用似乎不相关联立估计全林分生长模型参数，这样能够提高参数估计的有效性和一致性，减少系统估计误差。
（2）组合预测方法在提高模型预测精度方面有很好的表现。该方法充分利用单项预测模型所提供的有效信息，减少单个模型中随机因素的影响，把不同的模型误差分散化，从而提高预测精度。研究结果表明，组合预测模型精度（R2=0.9298）比单木模型（R2=0.9255）、林分模型（R2=0.9282）、分布模型（R2=0.9244）的预测精度都要高。利用组合预测估计方法预测林分断面积，使三个不同水平模型所得的林分断面积组合成一个预测值，保证了林分断面积预测的一致性，解决了不同预测模型间的相容性问题，为林分断面积生长模型一体化的研究提供了可行性。在组合预测模型中，权重的选取对提高组合预测结果的精度至关重要。相对于本研究所利用的误差平方和法和方差协方差法，最优加权法能够去除单项预测在组合预测模型中有偏的影响，从而使得组合预测达到无偏，最终达到提高预测精度的目的。
（3）解聚法以单木水平模型所得的林分变量尽可能地与林分水平模型所得的林分变量相匹配为迭代目标，进而调整单木生长模型以提高预测精度。本研究利用3种不同的解聚法（指数法，比例调整法，可加法）进行调整油松单木枯损，研究结果表明：这3种方法都提高了单木枯损的预测精度，可加法相对好于其它2种方法。相对于这2种迭代求解调整系数的方法，可加法直接通过调整系数公式计算得到，计算更加简单、有效。同时，在研究中我们也发现林分密度模型预测的精度在解聚法中起到重要的作用。林分株数密度预测精度高，那么就可以减少不同单木枯损预测方法的差别。组合预测法综合利用了不同水平模型所提供的信息，分散预测误差，进而提高林分变量预测精度。本研究中，我们结合解聚法和组合预测法调整单木枯损模型，研究结果表明综合利用这两种方法调整单木枯损，着实提高了单木枯损的预测精度。
（4）林分枯损和进界是描述林分动态变化特征的重要因子。然而，调查间隔期内可能有大量的样地没有发生林分枯损或进界现象，这意味着在所研究的数据中包含有大量的零数据，即数据结构是离散的。如果继续用最小二乘方法分析，估计不准确，会产生较大的偏差。本研究以计数类模型为基础，分别利用Poisson回归模型、负二项模型、零膨胀模型和Hurdle模型拟合林木枯损株数和林木进界株数，并通过AIC值，Pearson残差图以及Vuong检验对这些模型进行了详细分析比较。研究结果表明：Poisson回归模型不适用于模拟林木枯损株数。负二项回归模型相对于Poisson回归模型，比较适用。但是对于零枯损过多的数据，这两类模型拟合效果较差。零膨胀模型和Hurdle模型对这类数据有很好的解决办法。其中，零膨胀负二项模型和Hurdle-负二项模型拟合效果优于其它几种模型，而且这两个预测模型表现相当。本研究得出的结果可为分析林分枯损或者进界提供了一种可行性方法。
最后，利用C#.NET设置界面，通过SAS的IOM编程接口，实现了油松林分生长、枯损和进界动态变模型的系统集成。
The forest is the main body of terrestrial ecosystem. It plays a very crucial role inmaintaining ecological balance, improving ecological environment, as well as regulating globalclimate change. It is very important to forecast and evaluate forest resource accurately in timefor managing forest reasonably. The key problem of monitoring forest is how to know thedynamic change of foret growth, mortality and recruitment. As we know, the modelingtechnique is the basic method for knowing the forest dynamic change. Based on the forestdynamic models, we can know fully the forest development mode, which is helpful to monitorforest effectively and mange forest in reason. The dynamic models are composed of forestgrowth model, mortality model and recruitment model. In this study, based on the permanentdata of Chinese pine (Pinus tabulaeformis Carrière), the forest dynamic models includinggrowth, mortality and recruitment were developed using the modern biomathematics modeland statistical analysis method:
(1) The annual individual tree diameter model was developed with constant rate methodand variable rate method. Results showed that the variable rate method (RMSE=1.0182,R2=0.9310) outperformed the constant rate method (RMSE=1.1393, R2=0.9136) in predictingfuture individual tree diameter growth because the former accounted for the variable rate ofannual diameter growth, which was caused by changes of stand (basal area, dominant height)and tree attributes. It reflects the fact of tree growth. Also the whole stand models wereestablished with the variable rate method, which provided the annual forest stand changes. Theparameters of stand models were estimated via seemingly unrelated regression (SUR). Basedon the estimation method, the parameters had no obvious biases, and the precision of parameterestimation was more effectively.
(2) Forest combination method is a good method for improving model performance. Itefficiently uses information generated from different models to improve predictions byreducing errors from a single model. Results showed that the forecast combination method (R2=0.9298) provided overall better predictions of stand basal area than tree level model(R2=0.9255), stand level model (R2=0.9282) and distribution model (R2=0.9244). It alsoimproved the compatibility of stand basal area growth predicted from models of differentresolutions. In other words, it resolved the inconsistency of stand variable predictions atdifferent levels. It provided a method for integration of stand basal area. But we should alsorecognize that the method of calculating weights in combined models is very important. If themethod for calculating weights is good, then we will get the better results for combined model.In this thesis, the sum of squared errors method, variance-covariance method and optimalweight method were used to calculate the weights. The optimal weight method was superior toother two models, which removes the biased impact of single model on combined model, andthen gets the unbiased estimators.
(3) Disaggregation is a good method for improving prediction of tree models. In thismethod, individual-tree model predictions are adjusted so that the resulting sums would matchoutputs from a stand-level model. In this research, three disaggregation methods were used foradjusting tree mortality, which are power function method, proportional adjustment method,and addition method. Results showed that the disaggregation approach improved theperformance of tree survival models and the addition method performed slightly better than theother two disaggregation methods. An advantage of the addition method is that it alloweddirect computation of the adjusting coefficient, whereas the other methods required that theadjusting coefficient be resolved in an iterative manner. Meanwhile, we also showed thatstand-level prediction played a crucial role in refining outputs from a tree survival model,especially when it is a very simple model. Because the forecast combination method producedbetter stand-level prediction, we prefer the use of this method in conjunction with thedisaggregation approach, even though the performance gain in using the forecast combinationmethod shown for this data set was modest. And the results showed that the tree mortalityprediction was improved using the two methods together.
(4) Stand mortality and recruitment are very important variables for describing the standcharacters. Considering the fact that in permanent sample plots a relatively high number of the plots have no occurrences of recruitment or mortality even over periods of several years, itmeans that data are bounded and characteristically exhibit varying degrees of dispersion andskewness in relation to the mean. Additionally, the data often contain an excess number of zerocounts. Yet least squares method implicitly presumes that the data are Gaussian distributed withconstant variance, or at least satisfy the Gauss-Markov conditions. If the method is still used todeal with the data with large proportion of zero counts, the estimated results will be biased.Based on the theory of count models, poisson model, negative binomial model, zero-inflatedmodels and Hurdle models were used to analyze stand mortality and recruitment. The bestmodel was chose according to the AIC value, Pearson redidual plot and vuong test. Resultsshowed that: Poisson model was not suitable for stand mortality and recruitment, and negativebinomial was superior to the Poisson model. But both of them were not competent for theover-dispersion data. Zero-inflated model and hurdle model were fitted into the data.Additionally, zero-inflated negative binomial model (ZINB) and Hurdle-negative binomialmodel (HNB) outperformed than other models. The two models performed similarly inmodeling stand mortality and recruitment. The result provided a feasible method for analyzingstand mortality and recruitment.
Finally, integration system of forest growth, mortality and incruitment dynamic modelsfor Chinese pine was implemented. System interface was setup based on the C#. NET, linkedwith SAS through the SAS IOM programming.
引文
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