Generalized height–diameter models—an application for major tree species in complex stands of interior British Columbia

Using permanent sample-plot data, selected tree height and diameter functions were evaluated for their predictive abilities for major tree species in complex (multiple age, size and species cohort) stands of interior British Columbia (BC), Canada. Two sets of models were evaluated. The first set included five models for estimating height as a function of individual tree diameter, the second set also included five models for estimating height as a function of individual tree diameter and other stand-level attributes. The inclusion of the BAL index (which simultaneously indicates the relative position of a tree and stand density) into the base height–diameter models increased the accuracy of prediction for all species. On average, by including stand level attributes, root mean square values were reduced by 30.0 cm. Based on the residual plots and fit statistics, these models can be recommended for estimating tree heights for major tree species in complex stands of interior BC. The model coefficients are documented for future use.     

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.     

Regional mixed-effects height–diameter models for loblolly pine (<Emphasis Type="Italic">Pinus taeda</Emphasis> L.) plantations

A height–diameter mixed-effects model was developed for loblolly pine (Pinus taeda L.) plantations in the southeastern US. Data were obtained from a region-wide thinning study established by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Tech. The height–diameter model was based on an allometric function, which was linearized to include both fixed- and random-effects parameters. A test of regional-specific fixed-effects parameters indicated that separate equations were needed to estimate total tree heights in the Piedmont and Coastal Plain physiographic regions. The effect of sample size on the ability to estimate random-effects parameters in a new plot was analyzed. For both regions, an increase in the number of sample trees decreased the bias when the equation was applied to independent data. This investigation showed that the use of a calibrated response using one sample tree per plot makes the inclusion of additional predictor variables (e.g., stand density) unnecessary. A numerical example demonstrates the methodology used to predict random effects parameters, and thus, to estimate plot specific height–diameter relationships.     

Effects of competition and climate variables on modelling height to live crown for three boreal tree species in Alberta,Canada

Using tree data from permanent sample plots and climate data from the ClimateWNA model, mixed-effects height to live crown (HTC) models were developed for three boreal tree species in Alberta, Canada: trembling aspen (Populus tremuloides Michx.), lodgepole pine (Pinus contorta var. latifolia Engelm.) and white spruce (Picea glauca (Moench) Voss). Three model forms, the Wykoff model, a logistic model and an exponential model, were evaluated for each species. Tree height was the most significant predictor of HTC and was used in all models. In addition, we investigated the effects of competition and climatic variables on HTC modelling. Height–diameter ratio and either total stand basal area or basal area of coniferous trees were used as competition measures in the models. Different climate variables were evaluated, and spring degree-days below 0 °C, mean annual precipitation and summer heat–moisture index were incorporated into the aspen, lodgepole pine and white spruce models, respectively. Site index was only significant in lodgepole pine models. Residual variances were modelled as functions of tree height to account for heteroscedasticity still present in the mixed-effects models after the inclusion of random parameters. Based on model fitting and validation results as well as biological realism, the mixed-effects Wykoff models were the best for aspen and white spruce, and the mixed-effects logistic model was the best for lodgepole pine.     

An individual tree height increment model for mixed white spruce–aspen stands in Alberta,Canada

Individual tree-height increment models were developed for white spruce (Picea glauca (Moench) Voss) and aspen (Populus tremuloides Michx.) growing in the boreal mixed-species in Alberta. The models were formulated based on a selected base function (the Box–Lucas function), and the method of parameter prediction. Height increment was modeled as a nonlinear function of tree height, tree diameter, diameter increment, stand density, relative competitiveness of the tree in the stand, site productivity, and species composition. Since the data from permanent sample plots used in this study were time-dependent and cross-sectional, diagnostic techniques were applied to identify the models' error structure. Appropriate fits based on the identified error structure were accomplished using the nonlinear least squares procedures with a first-order autoregressive process. The models were also validated on independent testing data sets representing the population on which the models are to be used. Results showed that the average prediction biases were not significantly different from zero at α = 0.05, suggesting that the fitted models appropriately described the data and performed well when predictions were made. Biological implications of the variables that affect height increment in mixed-species stands were discussed.     

Wind speed and crown class influence the height–diameter relationship of lodgepole pine: Nonlinear mixed effects modeling

Wind-induced mechanical perturbation is one of the mechanisms determining the height–diameter relationship of trees, but its effects have largely been neglected in past height–diameter models. In this study, we examined the effects of including wind speed as a regressor in the height–diameter model for lodgepole pine (Pinus contorta var. latifolia Engelm.). We also tested the hypothesis that the height–diameter relationship differs between trees of different crown classes (dominant and subordinate trees), and that a mixed effects height–diameter model developed at the crown class level should achieve a better prediction than that developed at the plot level. The results showed that including wind speed significantly improved the fit of the height–diameter model. The results also showed that the height–diameter relationships differ significantly between the two crown classes. The mixed effects model developed based on crown classes of individual trees had better fit with reduced residual variance and decreased Akaike's information criterion and the Schwarz's Bayesian information criterion than the plot-based mixed model. Evaluation of the developed model suggests the crown class-based height–diameter model has better prediction in terms of prediction error and precision. The developed crown class-based mixed effects model can be used to provide more accurate prediction of tree heights for lodgepole pine from their diameters.     

A site dependent top height growth model for hybrid aspen

In this study height growth models for hybrid aspen were developed using three growth equations. The mean age of the hybrid aspen was 21 years (range 15?51 years) with a mean stand density of 946 stems...     

Estimation of stand attributes in <Emphasis Type="Italic">Cryptomeria japonica</Emphasis> and <Emphasis Type="Italic">Chamaecyparis obtusa</Emphasis> stands using QuickBird panchromatic data

This study aims to estimate stand density and stand volume in Cryptomeria japonica and Chamaecyparis obtusa stands from high-resolution satellite data and verify the reliability and uncertainty of the data. Sixty circular sample plots of 0.04 ha each were established. Their stand densities were estimated from the number of tree crowns derived from high-resolution satellite data using the watershed method. Stand densities derived from field surveys in the sample plots were compared with those obtained from high-resolution satellite data by stand age class. As a result, there was a positive correlation between them for sample plots of 41 years of age and over (R = 0.82); however, there was no correlation between them for sample plots of 40 years and under. Individual diameters at breast height (DBH) were estimated from crown areas obtained from high-resolution satellite data for the two species. Using the estimated DBH, individual tree heights were predicted from the height–diameter curves. Stand volumes were estimated from the sum of individual volumes, which were derived from volume formulas having two variables, i.e., DBH and height. Stand volumes derived from the field survey were compared with those obtained from high-resolution satellite data. The correlation coefficient between them for stands of 41 years of age and over was 0.78.     

Allometric model of the height–diameter curve for even-aged pure stands of Japanese cedar (<Emphasis Type="Italic">Cryptomeria japonica</Emphasis>)

We derived an allometric model of the height–diameter curve for even-aged pure stands, which was a modification of the earlier model proposed by Inoue (2000a). An individual-dependent allometric equation was used as the height–diameter curve. Using the discriminant analysis method, all trees composed of a stand were stratified into upper and lower trees. It was assumed that both relationships between mean tree height H _m and upper tree height H _u and between mean DBH D _m and mean DBH of upper trees D _u could be described by the time-dependent allometric power equations. The height–diameter curve showed an average relationship between tree height and DBH of a given stand at a given time, and hence it could be assumed that the height–diameter curve contained two points (D _m , H _m ) and (D _u , H _u ). With these assumptions, we derived an allometirc model of height–diameter curve, which allowed the coefficients of the curve to be estimated from mean tree height and mean DBH. The proposed model was fitted to Japanese cedar (Cryptomeria japonica D. Don) data. The error ratio of the allometric model ranged from 2.254% to 13.412% (mean = 6.785%), which was significantly smaller than that of the earlier model. When the error of mean tree height was ±1.0 m or less, the effect of the error of mean tree height on the error ratio was comparatively small. This suggested that the error of ±1.0 m in mean tree height could be accepted in the estimation of height–diameter curve using the allometric model. These features enable us to combine the allometric model with Hirata’s vertical angle-count sampling or growth models. In conclusion, the allometric model would be one of the most practical and convenient approaches for estimating the height–diameter relationship of even-aged pure stands.     

A simple step-wise procedure for predicting stand development of Acacia mangium plantations based on the maximum size–density line in South Sumatra, Indonesia

A simple step-wise procedure for predicting the course of stand development on log–log coordinates of stand density and quadratic mean diameter was presented based on a distance of measurement from the maximum size–density line of Acacia mangium. This procedure first predicts annual increment of diameter with a multiple linear regression having the distance, site index, and current diameter as independent variables, and then the associated mortality is calculated with the rate of reduction in stand density to the diameter growth derived from a fitted trend with the distance. The cumulative predictions, starting at 3 years after planting until 9 years of age, agreed well with the observations of group-age means of measurements calculated for the three levels of initial density. Contrasting trend of basal area growth between the three levels of initial density and those for their site index: the differences were decreasing in the former while they remained constant in the latter, was clearly illustrated with the procedure indicating a good potential for use in yield prediction. The simulations for stand growth under different spacing and thinning options were demonstrated in a stand density control diagram suggesting reasonable flexibility for practical application.     

基于多水平非线性混合效应蒙古栎林单木断面积模型

以吉林省汪清林业局184块样地中的10 111株蒙古栎为例,首先选用线性函数、Richards函数、Logistic 函数、指数函数等7种常用函数形式,分析4个因变量(后期胸径、后期胸高断面积、直径增量和胸高断面积增量)与前期胸径的影响,确定一个用于构建混合效应模型的基础模型。然后确定同时考虑林场效应和林场与样地交互效应时基础模型中最优的形式参数构造形式,利用逐步回归方法确定模型中所包含的林分变量,并分析和比较用来消除异方差的3种常用残差方差函数(指数函数、幂函数和常数加幂函数),最后检验模型预测效果。结果表明:Wykoff模型且因变量为后期胸高断面积拟合效果较好,故作为基础模型;除前期胸高直径(D)外,当考虑坡度正切(ST),对象木胸高直径与样地算术平均直径的比(RAD),样地胸高总断面积(TBA),样地中大于对象木直径所有树木的胸高断面积和(GSBA),对象木胸高断面积与样地算术平均胸高断面积的比 (RABA)和对象木胸高断面积与样地胸高总断面积的比(RBA)等林分变量时能进一步提高模型预测精度;对于残差方差,指数函数、幂函数和常数加幂函数都能消除异方差,但幂函数效果最好;当模型同时考虑林场效应和林场与样地交互效应时预测精度最高。     

Response of branch growth and mortality to silvicultural treatments in coastal Douglas-fir plantations: Implications for predicting tree growth

Static models of individual tree crown attributes such as height to crown base and maximum branch diameter profile have been developed for several commercially important species. Dynamic models of individual branch growth and mortality have received less attention, but have generally been developed retrospectively by dissecting felled trees; however, this approach is limited by the lack of historic stand data and the difficulty in determining the exact timing of branch death. This study monitored the development of individual branches on 103 stems located on a variety of silvicultural trials in the Pacific Northwest, USA. The results indicated that branch growth and mortality were significantly influenced by precommercial thinning (PCT), commercial thinning, fertilization, vegetation management, and a foliar disease known as Swiss needle cast [caused by Phaeocryptopus gaeumannii (T. Rohde) Petr.]. Models developed across these datasets accounted for treatment effects through variables such as tree basal area growth and the size of the crown. Insertion of the branch growth and mortality equations into an individual-tree modeling framework, significantly improved short-term predictions of crown recession on an independent series of silvicultural trials, which increased mean accuracy of diameter growth prediction (reduction in mean bias). However, the static height to crown base equation resulted in a lower mean square error for the tree diameter and height growth predictions. Overall, individual branches were found to be highly responsive to changes in stand conditions imposed by silvicultural treatments, and therefore represent an important mechanism explaining tree and stand growth responses.     

Characteristics of aspen infected with heartrot: Implications for cavity-nesting birds

Phellinus tremulae is an important fungal decay agent common to aspen and a critical component to the cavity-nesting bird complex found in western aspen stands. Little information exists on the conditions that facilitate infection and spread of P. tremulae in aspen forests. I used Forest Inventory and Analysis (FIA) data to explore the relationships of several tree and stand characteristics to the presence and frequency of P. tremulae in aspen measured across several western states of the United States. Results suggest a strong relationship between tree age, tree diameter, and compacted crown ratio with infection frequency in trees while stand purity, canopy cover and stand age had a positive relationship with the occurrence of P. tremulae in forest stands containing aspen. Logistic regression modeling identified stand age as the only variable that increased the odds of predicting infection at the stand-level while all tree-level variables were included in the tree model. Data also show that infection rates in the study area were lower than in other parts of aspen's range, and that average size of infected trees was smaller in the study area than those reported elsewhere. These results have important implications to management of aspen for wildlife, especially for birds that use decayed aspen for nesting.     

Predicting individual tree mortality in northern hardwood stands under uneven-aged management in southern Québec, Canada

This study proposes a generalized linear mixed model to predict individual tree mortality in northern hardwood stands under uneven-aged management. The model is based on a complementary log-log (CLL) link function, and was calibrated using permanent-plot data. Tree vigor, stem product, diameter at breast height and stand basal area were tested as explanatory variables. A plot and an interval random effect were specified to account for spatial correlations. When compared with the traditional logit link function, the CLL facilitates the inclusion of the time factor. In this case study, there was an important variability of mortality predictions between the plots and the intervals for a given plot. The interval random effect is thought to be associated with catastrophic mortality. Since both tree vigor and stem product proved to be significant mortality predictors, we recommend that these variables be evaluated to increase the accuracy of mortality models.     

Estimating Pinus palustris tree diameter and stem volume from tree height,crown area and stand-level parameters

Accurate and efficient estimation of forest growth and live biomass is a critical element in assessing potential responses to forest management and environmental change. The objective of this study was to develop models to predict longleaf pine tree diameter at breast height （dbh） and merchantable stem volume （V） using data obtained from field measurements. We used longleaf pine tree data from 3,376 planted trees on 127 permanent plots located in the U.S. Gulf Coastal Plain region to fit equations to predict dbh and V as functions of tree height （H） and crown area （CA）. Prediction of dbh as a function of H improved when CA was added as an additional independent variable. Similarly, predic- tions of V based on H improved when CA was included. Incorporation of additional stand variables such as age, site index, dominant height, and stand density were also evaluated but resulted in only small improvements in model performance. For model testing we used data from planted and naturally-regenerated trees located inside and outside the geographic area used for model fitting. Our results suggest that the models are a robust alternative for dbh and V estimations when H and CA are known on planted stands with potential for naturally-regenerated stands, across a wide range of ages. We discuss the importance of these models for use with metrics derived from remote sensing data.     

桂西南马尾松人工林生长对不同强度采伐的动态响应

[目的]研究不同强度采伐下马尾松的生长动态,筛选适宜的采伐强度,为马尾松人工林近自然经营提供技术支撑。[方法]2007年10月在14年生马尾松人工林(保存密度1 100株·hm~(-2))内进行采伐试验,设置4个采伐强度,即保留密度分别为225、300、375、450株·hm~(-2),以不采伐为对照;其后,自2008年开始连续8 a,每2 a测定1次马尾松的胸径、树高、枝下高和冠面积等生长指标,并计算单株材积和林分蓄积量,应用方差分析和Duncan多重比较分析生长指标对不同采伐强度的动态响应。[结果]表明:采伐强度显著影响林分生长,其中,林分平均胸径、单株材积、冠面积的年均增长量随保留密度增大而减小,但均显著高于对照(P0.05)。采伐后第1 3年,马尾松冠面积增长量显著高于采伐后期,胸径则在采伐后第3 5年最高,而不同采伐强度对林分树高生长影响不明显。保留密度显著影响林分枝下高和蓄积量的动态变化,其年均增长量随密度增大而递增。5个处理间林分蓄积年均增长量的差异随林龄的增大而逐渐缩小。[结论]马尾松人工林生长对不同强度采伐的动态响应以树冠最敏感,冠面积首先陡然增大,进而引起胸径的快速生长。树高和枝下高在采伐后年均增量变化相对平稳。4个采伐强度均显著促进单株材积生长,而仅保留密度为225株·hm~(-2)的采伐对林分蓄积增长量影响显著。综合比较林分的单株材积和林分蓄积连年增长量,建议在桂西南15年生马尾松人工林近自然经营中宜选择300株·hm~(-2)的保留密度进行采伐。     

Basal area growth models for individual trees of Norway spruce, Scots pine, birch and other broadleaves in Norway

Distance-independent individual tree growth models based on about 30,000 observations from the National Forest Inventory and the Norwegian Forest Research Institute have been developed for the main tree species in Norway. The models predict 5-year basal area increment over bark for trees larger than 5 cm at breast height. Potential input variables were of four types: size of the tree, competition indices, site conditions, and stand variables including species, mixtures and layers. The squared correlation coefficient (R²) varied from 0.26 to 0.55. The accuracy of the models was tested by comparing the individual tree models with Norwegian diameter increment models. The accuracy is similar, but individual tree models forecast diameter distributions directly. The inclusion of species mixture and layer as variables increases the reliability of the models in mixed and in uneven-aged stands.     

Developing an airborne laser scanning dominant height model from a countrywide scanning survey and national forest inventory data

Abstract

An airborne laser scanning (ALS) dominant height model was developed based on data from a national scanning survey with the aim of developing a digital terrain model (DTM) for Denmark. Data obtained in the ongoing Danish national forest inventory (NFI) were used as reference data. The data comprised a total of 2072 measurements of dominant height on NFI sample plots inventoried in 2006–2007 and their corresponding ALS data. The dominant height model included four variables derived from the ALS point cloud distribution. The variables were related to canopy height, canopy density and species composition on individual plots. The RMSE of the final model was 2.25 m and the model explained 93.9% of the variation (R ²). The model was successful in predicting dominant height across a wide range of forest tree species, stand heights, stand densities, canopy cover and growing conditions. The study demonstrated how low-density ALS data obtained in a survey not specifically aimed at forest applications may be used for obtaining biophysical forest properties such as dominant height, thereby reducing the overall forest inventory costs.     

Diameter distribution,stem volume and stem quality models for grey alder (Alnus incana) in eastern Finland

Stand-level predictions of basal-areadiameter distributions, height, positions of lowestdead and live branches and stem-rot are provided forgrey alder in eastern Finland. The usability of modelswas tested by calculating the accuracy of predictedvolume characteristics. The data were collected from 33stands situated in the provinces of North Karelia andNorth Savo in eastern Finland. These stands wereregenerated naturally, but some have been managed. Oneto three angle-count sample plots were placedsystematically in each stand using a 1 m² ha^–1 basal-area factor. The models can beapplied in two settings: tree diameters are eithermeasured or not. The prediction of branch heightcharacteristics, especially height to the lowest deadbranch, proved problematic due to weak correlationsbetween these characteristics and other treedimensions. Compared to previous studies it was foundthat stem-rot was higher in grey alder than in sprucebut lower than in white birch.     

Biomass, basic density and biomass expansion factor functions for European beech (Fagus sylvatica L.) in Denmark

The objective of this study was to analyse the within-tree allocation of biomass and to develop biomass functions for above- and below-ground components of European beech in Denmark. Separate functions were developed for stem, branches, below-ground stump and root system, total above-ground biomass and total tree biomass. For each of these components or aggregate components, models were also developed for the average basic density of wood and bark. To enhance the versatility of the models, a function for estimating the biomass expansion factor (BEF) was also developed. The functions were based on 66 trees measured for total biomass. Model performance was evaluated based on 74 trees measured only for above-ground biomass. The trees were sampled in 18 different forest stands covering a wide range of tree sizes and stand treatments. Models were estimated using a linear mixed-effects procedure to account for within-stand correlations. The functions for biomass and BEFs included only diameter at breast height and total tree height for individual trees as predictor variables. Inclusion of additional variables reflecting site quality or stand density did not improve model performance. The functions for basic density included individual tree diameter, tree height and quadratic mean diameter as predictor variables, indicating an effect of stand density on the basic density of wood and bark.