Modeling height growth for teak plantations in Colombia using the reducible stochastic differential equation approach

Teak( Tectona grandis L.f.) plantations are increasingly being established in tropical regions to meet a rising demand for its highly valued timber. Teak plantations have been established in the Atlantic Coastal Plain region of Colombia, a region climatically suitable for teak growth by having a monsoon climate with a unimodal precipitation pattern. Tree diameter at breast height(DBH, 1.3 m above ground) and mean top height, periodically measured over a 17-year period in 44 permanent sampling plots of size 0.06 and 0.10 ha, were used in this study. A stochastic differential equation(SDE), along with a Bertalanffy–Richards-type height growth model, was used to model and estimate top height growth of teak plantations in Colombia. Environmental noise and height measurement errors were explicitly considered as the main uncertainty sources of mean top height growth. The best model for estimating mean top height, based on statistical performance and biological rationale, had the asymptote defined as a local parameter and the growth rate and shape specified as global parameters. This model outperformed its counterpart that had the growth rate specified as a local parameter and asymptote and shape as global parameters. The selected model also outperformed alternative approaches such as the mixed-effects model, generalized algebraic difference approach, and the dummy variable method. Estimated trajectories for the mean top height of teak in Colombia are biologically sound based on the measured height series and previous studies in Latin America. Results suggest that most of the uncertainty associated with the mean top height growth of teak plantations in Colombia was largely explained by environmental noise. The best estimated model using the SDE approach can be useful for predicting height growth and evaluating site productivity of teak plantations in Colombia and in neighbouring countries with biophysical characteristics similar to those where teak has been planted in Colombia.     

Additive mixed models to study the effect of tree age and climatic factors on stem radial growth of Eucalyptus trees

The effect of tree age and climatic variables on stem radial growth of two hybrid clones of Eucalyptus was determined using longitudinal data from eastern South Africa.The stem radius of was measured weekly as the response variable.In addition to tree age,average weekly temperature,solar radiation,relative humidity and wind speed were simultaneously recorded with total rainfall at the site.An additive mixed effects model that incorporates a non-parametric smooth function was used.The results of the analysis indicate that the relationship between stem radius and each of the covariates can be explained by nonlinear functions.Models that account for the effect of clone and season together with their interaction in the parametric part of the additive mixed model were also fitted.The interaction between clone and season was not significant in all cases.For analyzing the joint effect all the covariates,additive mixed models that included two or more covariates were fitted.A significant effect of tree age was found in all cases.Although tree age was the key determinant of stem radial growth,weather variables also had a significant effect that was dependent on season.     

Using a stand-level model to predict light absorption in stands with vertically and horizontally heterogeneous canopies

Background： Forest ecosystem functioning is strongly influenced by the absorption of photosynthetically active radiation （APAR）, and therefore, accurate predictions of APAR are critical for many process-based forest growth models. The Lambert-Beer law can be applied to estimate APAR for simple homogeneous canopies composed of one layer, one species, and no canopy gaps. However, the vertical and horizontal structure of forest canopies is rarely homogeneous. Detailed tree-level models can account for this heterogeneity but these often have high input and computational demands and work on finer temporal and spatial resolutions than required by stand-level growth models. The aim of this study was to test a stand-level light absorption model that can estimate APAR by individual species in mixed-species and multi-layered stands with any degree of canopy openness including open-grown trees to closed canopies. Methods： The stand-level model was compared with a detailed tree-level model that has already been tested in mixed-species stands using empirical data. Both models were parameterised for five different forests, including a wide range of species compositions, species proportions, stand densities, crown architectures and canopy structures. Results： The stand-level model performed well in all stands except in the stand where extinction coefficients were unusually variable and it appears unlikely that APAR could be predicted in such stands using （tree- or stand-level） models that do not allow individuals of a given species to have different extinction coefficients, leaf-area density or analogous parameters. Conclusion： This model is parameterised with species-specific information about extinction coefficients and mean crown length, diameter, height and leaf area. It could be used to examine light dynamics in complex canopies and in stand-level growth models.     

‘Relationships between relationships’ in forest stands: intercepts and exponents analyses

Relationships between diameter at breast height(dbh) versus stand density, and tree height versus dbh(height curve) were explored with the aim to find if there were functional links between correspondent parameters of the relationships, exponents and intercepts of their power functions. A geometric model of a forest stand using a conic approximation suggested that there should be interrelations between correspondent exponents and intercepts of the relationships. It is equivalent to a type of ‘relationship between relationships’ that might exist in a forest stand undergoing self-thinning, and means that parameters of one relationship may be predicted from parameters of another. The predictions of the model were tested with data on forest stand structure from published databases that involved a number of trees species and site quality levels. It was found that the correspondent exponents and intercepts may be directly recalculated from one another for the simplest case when the total stem surface area was independent of stand density. For cases where total stem surface area changes with the drop of density, it is possible to develop a generalization of the model in which the interrelationships between correspondent parameters(exponents and intercepts) may be still established.     

Spatio-temporal Variation of Distribution Patterns in Cunninghamia lanceolata Plantations

To aid in management of Cunninghamia lanceolata,the main timber species in Southern China,its variation of spatial distribution pattern was analyzed.Three permanent plots of C.lanceolata plantations with approximately the same site conditions,set by China continuous forest inventory in Shunchang,Fujian,were selected. C.lanceolata growth was divided into two stages: young trees(5 cm≤diameter at breast height (DBH)<10 cm) and mature trees(DBH≥10 cm). The DBH and coordinates of every tree(DBH≥5 cm) in the permanent plots were recorded in 2003 and 2008.The function L(r),improvement of Ripley’s K(r),the paircorrelation function g(r),and the uniform angle index(W_i) were used to analyze the spatio-temporal variation of spatial distribution patterns.The three permanent plots had mean uniform angle index(W) between 0.494-0.578 at low altitudes,0.465-0.477 at medium altitudes,and 0.426-0.601 at high altitudes.Results showed that altitude did not affect the spatial distribution pattern. The L(r ) and g(r) function curves of mature trees were generally lower than young trees’,i.e.tend to be more random or uniform distribution.So regardless of the initial distribution of young or mature trees,with the passage of time,there was a tendency for the aggregated distribution to change to a random distribution,and a random distribution to change to a uniform distribution.     

ANALYSIS OF THE THERMOPHYSICAL PARAMETERS OF MOIST WOOD PARTICLE MATERIAL IN A COUPLED HEAT AND MASS TRANSFER PROCESS OF FREEZING BY USING FINITE ELEMENT METHOD

he coupled heat and moisture transfer in a freezing process of wood particle mate-rial was mathematically modeled in the paper.The models were Interactively solved by using thenumerical method(the finite element method and the finite difference method).By matching thetheoretical calculation to an experiment,he nonlinear problem was analyzed and the variablethermophysical parameters concerned was evaluated.The analysis procedure and the evaluation ofthe parameters were presented in detail.The result of the study showed that by using the method asdescribed in the paper,it was possible to determine the variable(with respect to temperature,mois-ture content and freezing state)thermophysical parameters which were unknown or difficult tomeasure as long as the governing equations for a considered process were available.The methodcan signifieantly reduces the experiment efforts for determining thermophysical parameters whichare very complicated to measure.The determined variable of the effective heat conductivi     

Effects of phosphorous fertilizer on seedlings growth and nodulation capabilities of some popular agroforestry tree species of Bangladesh

An experiment was conducted to assess the effect of Phosphorous （P） fertilizer （i.e. TSP or triple super phosphate @ 80 kg/hm^2） on seedling growth and nodulation capabilities of three potentially important agroforestry tree species （Acacia auriculiformis, Albizia lebbeck and Albizia procera） of Bangladesh. The study was conducted in nursery beds with six-month-old polybag seedlings ofA. auriculiformis, A. lebbeck and A. procera. The effects of P fertilizer on seedling growth and nodulation were compared with that of the seedlings grown in control （i.e. unfertilized soil）. The observations revealed that the seedling growth was enhanced significantly with the application of P fertilizer. The growth was found more pronounced in A. auriculiformis, whereas it was not apparent and shows depressed growth in case ofA. lebbeck. The study also suggests that the nodulation in terms of nodule number and size was also increased significantly with the application of P fertilizer.     

华北沙地不同密度小黑杨林生长特征

The growth characteristics and correlation between the canopy index and growth characteristics of Populus×xiaohei plantation with different densities and stand ages were studied by the methods of sampling typical plot and allometric dimension analysis in Xuejiazhuang Forest Farm in Shanxi Province.The results showed that the DBHs of Populus×xiaohei plantations with various tree densities were different.The Logistic growth model could accurately describe the tree height and DBH growth of Populus×xiaohei.The ...     

Impact of irrigation regimes on regeneration and growth of Prosopis cineraria in arid areas of Indian Thar

An experiment was initiated in 2008 to evaluate the impact of irrigation regimes on germination and growth patterns of seedlings of Prosopis cineraria in the arid areas of Thar, India. Seeds collected from dried pods of P. cineraria were sown in polybags placed in nursery beds. Different irrigation regimes were provided to different beds and data regarding germination and growth were recorded to study natural regeneration. The study revealed that irrigation regimes significantly affected the germination and growth of P. cineraria under nursery conditions. The germination rate declined as the irrigation regime shifted from a daily to a fortnightly basis. Height of the seedlings also declined with a decrease in the intensity of irrigation. Thus, it can be concluded that germination and growth of seedlings of P. cineraria under nursery conditions can be enhanced by providing irrigation at regular intervals.     

Optimizing continuous cover management of boreal forest when timber prices and tree growth are stochastic

Background: Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty.Methods: Both anticipatory and adaptive optimization approaches were used. The adaptive approach optimized the reservation price function instead of fixed cutting years. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years. Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of the deterministic diameter growth model were also simulated. They consisted of random tree factors and cross- and autocorrelated temporal terms.Results: Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty were included in the analyses.Conclusions: Adaptive optimization and management led to 6%–14% higher net present values than obtained in management that was based on anticipatory optimization. Increasing risk aversion of the forest landowner led to earlier cuttings in a mature stand. The effect of risk attitude on optimization results was small.     

Growth models and site index table of natural Korean pine forests

IntroductionKoreanpine(PinuskOraiensisSieb.etZucc.)isoneofthemostimportanttimberspeciesanditisnaturaIIydistributedinHeilongjiang,JiIinandLiaon-ingprovincesinChina.ManyforestryresearchersmadeextensiveandprofoundstudiesonthisspeciesJiangYiyin(1985)studiedthegroWthandgrowthmodelsforpIantationsofKoreanpine.However,veryfewpaperswerefoundonthegroWthmodeIsofnaturalKoreanpineforest.Koreanpinehasa1onggroWthperiod.ForextensivelymanagingKoreanpineforest,itneedstheJorestrytabIeswithhighac-Curacy…     

Comparison of the Chapman-Richards Function with the Schnute Model in Stand growth

IntroductionAsagrowthmodelforanindividualtreeorforeststhnd,theChapman-RichardsFunction,anextensiontotheVonBertalanffy'sgrowththeory(Bertalanffy1957)embodiesallotherestablishedgrowthfunction.ThisfunctionhasbeenwideIyusedinforestrybecauseofitsflexibility,ac…     

吉林蛟河针阔混交林主要树种树高-胸径模型

[目的]建立吉林蛟河针阔混交林主要树种不同竞争强度个体的树高-胸径关系模型,并探讨竞争强度对树高-胸径关系的影响。[方法]采用蛟河42 hm2成熟林固定样地中4个树种的树高-胸径数据,用Chapman-Richards、Logistic、Korf和Weibull模型这4种应用广泛的经验模型进行树高-胸径曲线拟合,选出适合的最佳模型。[结果]表明:(1)4个树种的12组个体中有7个组的最佳模型形式是Weibull模型,4个组的最佳模型形式为Chapman-Richards模型,只有1组为Korf模型。(2)同一树种的低竞争强度个体和高竞争强度个体的最优模型形式不同。(3)用独立样本数据对最优模型进行检验,模型表现良好。[结论]Weibull模型能够很好地拟合4个树种各竞争强度的树高-胸径关系,能够适用于本地区针阔混交林的树高-胸径模拟,并且竞争强度会影响树高-胸径关系,将各竞争强度个体分别进行树高-胸径拟合可以提高模型预测能力。     

福建省火炬松人工林生长特性的研究

对福建省火炬松人工林生长特性以及不同栽培区火炬松的生长规律进行了对比分析。结果表明 :Richards函数是福建省火炬松优势木生长的最佳模型 ;对树高曲线方程而言 ,h=a0 da1 最符合火炬松树高随直径变化的规律。随着栽培区适宜程度的降低 ,火炬松胸径生长量随之降低 ,胸径平均生长量、材积连年生长量达到最大值的年龄也随之提早。     

安徽省青阳县栎类阔叶林树木生长规律研究

本文以46年生栎类解析木为基础,运用DPS统计软件进行回归分析,分别采用Logistic、Richards、Compertz、Mitscherlich、Gauss、Log-modified、Density7种理论方程与二次曲线对栎类进行拟合,建立栎类树高、胸径、材积的最优数学模型,对其生长规律进行分析。结果表明：建立的生长模型中Richards方程拟合效果最好、精度最高。故选择Richards方程为栎类树高、胸径、带皮材积、去皮材积生长模型。栎类树高的平均生长量在20年时达到最大值,而树高的连年生长量最大值出现在14年,在20年时平均生长量与连年生长量相等。栎类胸径的连年生长曲线与平均生长曲线在24年时相交。栎类材积生长量在14年前生长较缓慢,在46年内还未出现材积平均生长量的最大值。材积的连年生长量曲线与平均生长量曲线在46年内还未相交,说明其未达到成熟龄。探讨了安徽省青阳县天然次生栎类阔叶林的生长规律,为栎类阔叶林合理利用和培育提供参考。     

Genetic variation in height growth curves observed in three clonal tests of sugi (Cryptomeria japonica D. Don) in Kyushu

Genetic variation in the height growth curves was investigated by analyzing data from three clonal trials of sugi (Crytomeria japonica D. Don) in Kyushu. Average height of twelve clones measured at each of five years until 30 years of age were fitted to the Chapman-Richards function with two parameters model. Clonal variation in the two parameters (an upper asymptote and a rate of growth parameter) was statistically significant across the tests, indicating that height growth pattern is under genetic control. The type of growth curve was clearly classified with the two parameters and agreed with the empirical classifications of the growth habit of local varieties. The rate of growth parameter was correlated with total height up to 20 years of age, while the upper asymptote was correlated only with the last ten years’ increment from 21 to 30 years where the clonal repeatability was decreasing. This indicates that a clonal selection for long rotation management system would not be reliable unless the height is measured accurately with more advanced devices or it is adjusted by the current increment of diameter.     

基于异速生长和理论生长方程的广东省木荷生物量动态预测

【目的】将异速生长方程与理论生长方程相结合,预测广东省木荷生物量动态,为广东省木荷林碳汇计量提供模型和方法,为其他树种碳汇计量提供可借鉴的方法学支持。【方法】基于实测样木生物量调查数据,包括40株树干解析资料,构建由胸径和年龄的理论生长方程以及地上生物量和胸径的异速生长方程组成的模型系,利用非线性度量误差联立方程组,在胸径生长速度分级情况下拟合模型参数;基于3期森林资源连续清查固定样地样木数据,对广东省木荷生物量动态进行预测。采用决定系数( R 2)和均方根误差(RMSE)评价模型拟合效果,通过生物量存量估计误差和增量估计误差判断模型预测效果。【结果】在胸径生长速度分级情况下,理论生长方程中年龄对胸径的解释率达0.95以上,比不分级提高0.166 3,均方根误差下降到1.97 cm,降低2.16 cm以上,预测胸径对地上生物量的解释率提高到近0.82;接近独立异速生物量模型中实测胸径对地上生物量的解释率达0.88以上,比不分级提高近0.30,均方根误差下降到51 kg左右,下降30 kg以上。在胸径生长速度不分级情况下,各期生物量存量估计误差变动幅度在-46.31%~77.45%之间,而分级情况下下降到-16.13%~7.06%;在尺度上,分级与不分级均呈相同规律,即单木误差小于林分误差、林分误差小于区域误差。不分级时,单木水平和区域尺度间的误差不大于10%,而分级时小于8%。不同间隔期生物量增量估计误差,不分级时估计值普遍偏大,在32.57%~115.45%之间,而分级时下降到-6.57%~15.77%之间,在单木尺度上不超过±10%;随着尺度增大,增量估计误差不断增加,不分级时单木水平和区域尺度间的误差介于10%~15%之间,分级时稳定在8%左右。【结论】对于理论生长方程和异速生长方程组成的模型系,分级可极大提高模型精度,减小预测估计误差;生长速度不分级时,仅利用胸径或年龄数据,分级时,则可利用2期胸径数据或1期胸径和年龄数据,就可预测未来生物量动态,简单方便,在森林资源连续清查和碳汇造林的碳汇量计量中具有极大应用价值,区域尺度上的估计误差也可基本满足精度要求。     

四川香樟人工林生长特性研究

对四川香樟树高、胸径、材积生长规律研究结果表明：香樟生长适应性较强,27 a树高平均可达15.80 m,胸径可达35.1 cm,材积可达0.6790 m3;香樟造林初期生长相对较缓慢,在10 a～12 a时树高和胸径连年生长量到达峰值,之后开始下降但仍保持较高的年生长量;材积连年生长量和平均生长量随着树龄的增大而呈持续增长趋势,27a时,仍维持较快的增长速度;Logistic曲线对香樟树高、胸径和材积生长动态有较好的拟合效果,其回归方程分别为：y=35.4356/（1＋11.59×e-0.1942x）,y=16.429/（1＋12.6749×e-0.1906x）,y=0.9639/（1＋107.5×e-0.2043x）。     

Development of site index curves for Pinus kesiya in the Philippines

This study was conducted to develop a height–age growth model and site index curves for site quality evaluation of old secondary-growth stands of Pinus kesiya in the northern Philippines. The Chapman-Richards growth function was used in the guide curve method to generate anamorphic site index curves for this species. In order to evaluate the developed model, coefficient of determination (R ² ), root mean square error (RMSE), bias (ē), absolute mean difference (AMD) and mean percent bias (MPB) were used as statistical criteria. The Chapman-Richards model explained about 96.84% of the total variation of the dominant height. The value of ē was ?0.004 m, AMD was 2.566 m, MPB was 3.88% and RMSE was 3.331. The site index curves developed as a result of this study are significant for forest managers in predicting the growth patterns and classification of site productivities for Pinus kesiya stands.     

黄甜竹丰产林地下竹鞭结构生长规律研究

本文通过对黄甜竹丰产林16块标准地的地下竹鞭、地上竹高、胸径等因子的系统调查,了解黄甜竹地下竹鞭的结构、生长规律以及在土层中分布情况,并分析黄甜竹生物量与竹高、胸径等林分各因子的相互关系,采用线性回归和幂函数方程对其生物量进行数学模型拟合,讨论并论述了改善林下竹鞭结构的生长发育规律和提高黄甜竹生物量的指导方法,从而为黄甜竹丰产栽培技术研究提供科学的理论依据.