基于混合效应的湖南栎类与杉木单木断面积生长模型研究

构建栎类（Quercus sp.）杉木（Cunninghamia lanceolata）混交林单木断面积生长模型,为该类 型林分的生产经营提供参考。以湖南省 31 个样地共 1 646 株栎类与 1 154 株杉木为研究数据,7 个常见模 型作为栎类、杉木的单木基础模型,基于样地随机效应构建栎类、杉木的单木断面积混合效应模型。结果 表明,栎类断面积的最优基础模型为 Gompertz,杉木断面积的最优基础模型为 Logistic;栎类断面积混合 效应模型相比于基础模型,决定系数 R2 提高了 0.053,SSE 与 RRMSE 均有所降低;杉木断面积混合效应 模型相比于基础模型,决定系数 R2 增加了 0.035,SSE 与 RRMSE 均有所降低;栎类断面积的成熟年龄在 50 年以后,杉木断面积的生长速率在 30 年左右逐步放缓。文章在栎类、杉木单木模型的基础上进一步加 入样地随机效应,模型拟合精度明显提高,说明栎类、杉木的断面积生长都受到年龄与样地的综合影响。     

含间伐强度哑变量的关帝山油松天然林单木断面积生长模型构建

以关帝山林区9块油松天然林固定样地为研究对象,选择4种具有生物学意义理论生长方程,构建包含立地条件、年龄及竞争指标的油松单木断面积基础模型,将间伐强度作为哑变量引入模型,比较模型拟合效果的差异。结果显示:单木断面积基础模型决定系数R~2为0.46～0.52,P值为0.89～0.92,含间伐强度哑变量的单木断面积生长模型R~2和P值均有显著提高,分别为0.51～0.61和0.95～0.99;含间伐强度哑变量的Weibull方程拟合效果最优,其模型R~2为0.606 1,P值为0.991 2。含哑变量的油松单木断面积生长模型可以有效解决间伐类型差异对断面积预估的影响,提高建模精度与模型适用性。     

基于林层哑变量的湖南栎类天然次生林断面积生长模型

【目的】基于栎类天然次生林林层分异现象,分析林层效应对林分断面积生长的影响,以林层效应为哑变量建立栎类天然次生林断面积生长模型,为更有效地经营管理湖南栎类天然林提供参考与依据。【方法】基于湖南省内设置的栎类固定样地51块,以调查的样地数据,从6个具有生物学意义的备选模型中选出一个最优基础模型。通过国际林联(IUFRO)的优势高划分、全树高聚类与光竞争高度法划分林层后,以最优模型分别对全林分及主林层、次林层断面积进行拟合,选出最优林层划分方法;根据林层划分结果,构建含林层效应哑变量的林层断面积生长模型。【结果】3种林层划分方法的划分结果均能满足国标(GBT 26424—2010)的要求;断面积生长模型的最优形式为Schumacher形式的模型,林分断面积模型的确定系数(R~2)为0.925 5,各林层断面积模型的确定系数(R~2)均在0.95以上,栎类林最优林层划分方法为国际林联(IUFRO)法,根据其划分结果构建的断面积生长模型的确定系数(R~2)为0.972 1,采用林层效应作为哑变量构建断面积模型有效提升了模型精度,与不分层的全林分断面积模型相比,确定系数(R~2)提高了4.94%,平均绝对误差(MAE)降低了10.23%,总相对误差(TRE)降低了1.19%。【结论】构建含林层效应哑变量模型解决了林层效应对断面积生长预估的影响,同时减少了建模工作量,提高了模型的精度与适用性,对栎类林的林分生长收获与经营管理具有重要意义。     

湖南栎类-马尾松天然混交林单木生长模型研究

建立湖南栎类-马尾松天然混交林单木材积和断面积生长模型,为该林分的提质增量提供科学指导。选取湖南省9个地区共23块栎类-马尾松天然混交林,构建栎类、马尾松单木材积和断面积生长模型。通过分析可知:两种树种的材积和断面积生长模型均以Richards生长模型为最优,其确定系数(R~2)最高,残差平方和(SSE)最小;混合效应模型模拟结果显示,栎类单木材积和断面积生长模型的随机效应在参数a_1处最好,而马尾松的材积和断面积生长模型的随机参数分别为b_1和a_1+b_1;相比基础模型,混合效应模型的拟合精度(P)、确定系数均有所提高,平均误差(ME)、平均误差绝对值(MAE)、相对平均误差(RME)和相对平均误差绝对值(RMAE)均大幅降低。结果表明,天然林林木的材积和断面积生长受树种与立地类型差异的影响较大,而混合效应模型能够充分考虑立地之间的差异,可以很好地解决这一难题。     

基于非线性度量误差的湿地松生长模型

基于样地调查数据选用理查德方程和Schumacher为基础模型,采用非线性度量误差方法求解模型,在最优基础模型中引入哑变量,建立可兼用于采脂与未采脂林分的湿地松人工林生长模型。结果表明:两类基础模型的拟合效果均较好,模型决定系数均超过了0.9,其中Schumacher模型为最优基础模型。在该模型引入哑变量后,拟合出的断面积与蓄积量模型决定系数提升为0.9927与0.9972,模型精度提升为96.1%与97.2%。对哑变量模型做配对t检验,其p值均大于0.05,表明模型可用于估测采脂与未采脂不同经营措施湿地松林分断面积与林分蓄积量,可作为湿地松林分蓄积量测算与林分经营的依据。     

基于哑变量的湿地松林分断面积生长模型

[目的]为更好地估测福州市湿地松人工林林分断面积生长情况,同时为湿地松人工林的经营提供参考依据.[方法]基于样地调查数据选用理查德方程、逻辑斯蒂、Mitscherlich和Schumacher等基础模型,引入优势木平均高和年龄因子为自变量并将林分密度指数作为密度指标加入到基础断面积模型中.在最优基础模型中引入哑变量,建...     

湖南栎类天然混交林优势木树高曲线哑变量模型研究

使用13种具有代表性的树高-胸径模型对湖南栎类天然混交林优势木树高-胸径关系进行了拟合,从中筛选出拟合度较高的模型作为基础模型,以进一步构建含林分类型、立地类型哑变量的天然混交林优势木树高曲线模型。研究结果表明:平均优势木模型要优于最高优势木模型,利用哑变量模型拟合的效果要明显优于基础模型;n林分类型哑变量和立地类型哑变量平均优势木模型结构相同,都是H=1.3+(sun from n to i=1)a_i×Z_i×D_g/(D_g+1)+b×D_g,其确定系数分别为0.711 9和0.977 5,立地类型哑变量模型要优于林分类型哑变量模型。利用哑变量模型可提高模型精度及适用性,有助于建立区域性通用生物数学模型,并为全国栎类天然混交林立地质量评价的研究提供科学支撑和参考依据。     

基于哑变量的湖南栎类次生林直径分布研究

文章以湖南省188个栎类次生林样地为研究对象,利用Kolmoglov-Smirnov检验法对6种分布密度函数在直径分布拟合中的适用性进行检验。以林分变量为自变量,采用参数预测法构建Weibull函数3个参数的逐步回归参数模型和以林分类型为哑变量的哑变量参数模型,并对比两类模型的直径分布预测精度。结果表明,Weibull函数更适合于栎类直径分布的拟合(接受率为91.7%);与逐步回归参数模型相比,参数b、c的哑变量模型的R~2分别提高了0.104和0.134,且应用于直径分布预测时的精度显著提高(P=0.025)。研究基于林分类型哑变量构建参数模型,并用于栎类次生林的直径分布预测,预测精度较高。     

林分生长和收获模型整体化思路探讨

介绍了林分生长和收获模型的概念、分类及模型整体化研究的内涵,以单木直径生长模型作为基础模型,提出了单木直径、树高、断面积、材积模型之间,林分平均直径、断面积、材积模型之间以及单木生长模型、全林分模型和径阶分布模型之间的耦合思路,对于解决不同水平模型之间的相容性、一致性及内部结构的统一具有一定意义.     

华北落叶松与白桦混交林树高与胸径关系研究

【目的】建立华北暖温带华北落叶松与白桦针阔混交林树高与胸径关系的非线性混合效应模型,为研究针阔混交林中不同树种相互作用及其生长发育规律提供科学依据。【方法】以河北省塞罕坝机械林场的华北落叶松与白桦针阔混交林为研究对象,基于83块30 m×30 m的标准地调查数据,首先选取5个具有生物学意义的非线性树高与胸径关系基础模型进行拟合,确定最优基础模型;其次通过相关分析确定影响树高生长的主要因子;最后基于最优基础模型和主要因子建立包含哑变量的华北落叶松与白桦针阔混交林树高与胸径关系预测模型。【结果】在5个候选非线性树高与胸径关系模型中,Richard模型具有最好的拟合结果,其模型确定系数(R2=0.918 6)最大,均方根误差(RMSE=2.405 8)及绝对误差(Bias=0.194 5)最小;通过相关分析确定海拔和林分断面积与树高生长均在P 0.01水平上呈现显著性;基于基础模型构建了包含哑变量及主要影响因子的不同树种树高与胸径关系混合效应模型,当随机效应参数作用在林分断面积上时,模型预测精度较高。【结论】基于主要影响因子和包含哑变量的非线性混合效应树高与胸径关系预测模型,能够有效解决混交林中树种及主要因子对树高与胸径关系的影响,提高了预测模型的适用性及预测精度,为混交林森林质量精准提升提供科学依据。     

杉木人工林单木断面积生长动态模拟

应用面板数据固定效应模型对杉木人工林单木断面积生长规律进行模拟,在模拟过程中,将胸径(DBH)和活冠比例(LCR)作为自变量,又分别加入密度因子和不同类型的竞争指数,同时引入立地条件和林龄效应来解释单木断面积生长过程中的异质性。结果表明:虽然密度因子与竞争指数有较强的相关性,但是在单木断面积生长中都具有不可忽略的重要影响。立地条件与林龄对单木断面积的拟合偏差在不同的林分密度下略有不同,随立地指数或者林龄增加,其对平均单木断面积拟合偏差的影响也增大。     

抚育间伐对辽东山区3种林型林分总断面积和总收获量的影响

利用几十年的定位观测数据,分析了抚育间伐对辽东山区红松人工林、天然次生蒙古栎林和人工诱导的阔叶红松林3种林型林分总断面积和总收获量的影响。结果表明:与对照区相比,抚育间伐没有提高红松人工林的林分断面积和蓄积总生长量,但极强度和强度间伐能提高红松人工林的林分断面积生长率。林分总断面积随着间伐强度的增加先升高后降低,各间伐强度均能提高林分总断面积,极强度间伐除外。抚育间伐能提高红松人工林林分蓄积生长率,弱度区除外;红松人工林林分总收获量随着间伐强度的增加先升高后降低,各间伐强度均能提高林分总收获量,中度间伐效果最好。抚育间伐能提高蒙古栎林林分断面积和蓄积总生长量、生长率以及林分总断面积和总收获量,各指标随着间伐强度的增加先升高后降低,中度间伐效果最好。抚育间伐能提高人工诱导的阔叶红松林林分断面积和蓄积总生长量、生长率以及林分总断面积和总收获量,林分断面积和蓄积总生长量、林分总断面积和林分总收获量随着间伐强度的增加而升高,林分断面积和蓄积生长率随着间伐强度的增加先升高后略有降低,强度间伐效果最好。可见,合理的间伐强度能够提高3种林型的林分总断面积和总收获量。     

Stand volume functions for picea abies in western Norway

A material of 1156 observations was used to develop two Norway spruce (P. abies (L.) Karst.) stand volume functions for western Norway. An additive model initially based on a polynomial of second degree was found to be most suitable. The independent variables were stand basal area, Lorey's mean height, the product of basal area and mean height, and the square of the mean height.

In order to roughly reflect the different climatical conditions within western Norway, all municipalities were classified into the categories “inland” and “coast”. The individual observations were assigned the category of the municipality in which they were sited. The type of district was included in the selected additive model by means of a dummy variable approach. Testing showed that two individual regressions should be recommended for prediction purposes in the respective districts. R² was 0.998 and C.V. was less than 2.5%. The regressions fitted most parts of the material very well, with exception for low densities for inland districts. Testing by means of an independent data set indicated no systematic differences.     

基于混合效应的湖南马尾松次生林单木生长模型

[目的]建立湖南省马尾松次生林单木断面积与材积生长模型,为林木的生长预估提供理论依据.[方法]以湖南省2014年一类清查样地中的20块马尾松次生林为研究对象,选取5个具有生物学意义的生长方程,建立马尾松断面积和材积随年龄变化的基础模型,在此基础上,加入以样地为随机效应的随机参数,构建基于混合效应的湖南马尾松次生林单木断...     

A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.)

A nonlinear mixed-effects modelling approach was used to model the individual tree height–diameter relationship in pyrenean oak (Quercus pyrenaica Willd.). A set of 24,627 pairs of height–diameter measurements were used to fit the model. These were taken at 950 Spanish National Forest Inventory plots embracing six different biogeoclimatic strata. Eleven biparametric nonlinear height–diameter equations were evaluated to find a local model, which only includes the dimensions of the tree as explanatory variables. After selecting the local model, a regional or generalized model was studied. The following stand variables were tested for inclusion in the model as fixed effects: stand density, quadratic mean diameter, arithmetic mean diameter, dominant diameter, arithmetic mean height, dominant height and basal area. Dominant height and basal area of the stand were found to produce the most satisfactory fits in the stand model. Interregional variability was studied by including strata effects as dummy categorical variables and was analysed using the non-linear extra sum of squares method and the Lakkis–Jones test. Height–diameter models were found to be similar for the six biogeoclimatic strata. Finally, a mixed nonlinear model technique was applied to fit the definitive model. By calibrating the model it is possible to predict random components of definitive model from height measurements previously taken from a subsample of trees. The different alternatives tested reveal that only two or three trees are necessary to calibrate the model.     

Quantitative validation and comparison of a range of forest growth model types

Predictions from a range of model types (simplified process-based, a statistical state space, statistical difference, and a hybrid model) were compared to 969 measurements of forest growth across an environmental gradient. The models compared were 3-PG, CANTY, CanSPBL(1.2), and CanSPBL(water). The study made an objective comparison and validation of model types, with the main criterion for comparison being each model's ability to match actual historical measurements of forest growth in an independent data set. A number of stand level forest growth variables were compared including basal area, mean top height, and stocking over 14,058 ha of plantation-grown Pinus radiata in south-eastern New Zealand. Stand variable predictions at 195 permanent plot locations covering a range of elevations from 0 to 660 m were highly correlated with field estimates derived from plot data. The hybrid model CanSPBL(water) on average was the most accurate model in the study where predictions of stocking, basal area, and mean top height were 96%, 96%, and 96% efficient. The statistical-difference equation model CanSPBL(1.2) was equally efficient but on average 3% less accurate and slightly more biased in predictions suggesting that the hybrid model explained differences in growth due to differences water availability and soil type. The process-based model 3-PG predicted stocking and basal area 89% and 88% efficiently. Finally, the statistical state-space model CANTY predicted stocking, basal area, and mean top height 96%, 87%, and 87% efficiently. Results quantify the amount of precision that can be expected from the three model types, and suggest that each approach has strengths and weaknesses.     

A review of stand basal area growth models

Growth and yield modeling has a long history in forestry. The methods of measuring the growth of stand basal area have evolved from those developed in the U.S.A. and Germany during the last century. Stand basal area modeling has progressed rapidly since the first widely used model was published by the U.S. Forest Service. Over the years, a variety of models have been developed for predicting the growth and yield of uneven/even-aged stands using stand-level approaches. The modeling methodology has not only moved from an empirical approach to a more ecological process-based approach but also accommodated a variety of techniques such as: 1) simultaneous equation methods, 2) difference models, 3) artificial neural network techniques, 4) linear/nonlinear regres-sion models, and 5) matrix models. Empirical models using statistical methods were developed to reproduce accurately and precisely field observations. In contrast, process models have a shorter history, developed originally as research and education tools with the aim of increasing the understanding of cause and effect relationships. Empirical and process models can be married into hybrid mod-els in which the shortcomings of both component approaches can, to some extent, be overcome. Algebraic difference forms of stand basal area models which consist of stand age, stand density and site quality can fully describe stand growth dynamics. This paper reviews the current literature regarding stand basal area models, discusses the basic types of models and their merits and outlines recent progress in modeling growth and dynamics of stand basal area. Future trends involving algebraic difference forms, good fitting variables and model types into stand basal area modeling strategies are discussed.     

抚育间伐对人工红松林生长效应的影响

利用不同间伐强度后40 a的人工红松林,连续抚育3次的长期定位观测资料,分析了抚育间伐对人工红松单木胸径和材积、林分断面积和蓄积、林分枯损和总收获量的影响。研究结果表明:间伐可以增加单木平均胸径和材积的生长率,且不同间伐强度表现为相同的规律,即中度(33.2%)强度(43.4%)弱度(23.1%)对照(0.0%);间伐后林分的断面积和蓄积生长率,具有相似的自然规律,间伐样地的生长率均高于对照;林木枯损率随间伐强度的增加而降低;间伐后的林分总收获量平均增加11.6%,间伐林分之间差别不明显。在整个研究阶段,不同的抚育阶段表现不同的规律,抚育间伐可以延缓单木胸径和材积生长速度的降幅;而不同抚育阶段内,林分断面积和蓄积生长率均为增长,也就是说,在一定阶段内间伐可以有效地提高林分平均断面积和蓄积生长率;从林分枯损状况来看,应该减少间伐间隔期。     

A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria

Because of the gradual shift from pure even-aged forest management in central Europe, existing yield tables are becoming increasingly unreliable for forest management decisions. Individual tree-based stand growth modeling can make accurate stand growth predictions for the full range of conditions between pure even-aged and mixed-species uneven-aged stands. The central model in such a simulator is basal area increment for individual trees. Spatial information is not needed, and age and site index are intentionally not used to gain generality for all possible stand conditions. A basal area increment model is developed for all the main forest species in Austria: spruce (Picea abies), fir (Abies alba), larch (Larix decidua), Scots pine (Pinus sylvestris), black pine (Pinus nigra), stone pine (Pinus cembra), beech (Fagus silvatica), oak (Quercus robur, Quercus petraea and Quercus cerris), and for all other broadleaf species combined. The Austrian National Forest Inventory provided 5-year basal area increment from 44 761 remeasured trees growing on 5416 forested plots in the 1980s. This large sample is representative of forest conditions and forest management practices throughout Austria and therefore provides an excellent data base for the development of an increment model. The resulting increment model explained from 20 to 63% of the variation for all nine species and from 33 to 63% of the variation if the minor species Pinus cembra is excluded. These results compared quite closely with those of Wykoff for mixed conifer stands in the Northern Rocky Mountains. In the Austrian model, size variables (breast height diameter and crown length) accounted for 14–47% of the variation in basal area increment, depending on tree species. The best competition measure was the basal area of larger trees, which provides a tree-specific measure of competition without requiring spatial information; crown competition factor provided only minor improvement. Competition variables accounted for 9% of the variation on average, and up to 15% for some species. Topographic factors (elevation, slope, aspect) explained up to 3% of the variation, as did soil factors. Remaining site factors; such as vegetation type and growth district accounted for a maximum of 3% of the variation in increment. In total, site factors explained from 2 to 6% of the variation. Even though site factors account for a small percentage of the variation, they are not only significant, but serve to localize a particular prediction. These species-specific interrelationships between basal area increment and the various size, competition, and site varibles correspond quite well with ecological expectations and silvicultural understanding of these species in Austria. Because the sample base is so strong, the resulting growth models can be recommended not only for all of Austria but for surrounding regions with similar growth conditions.