Modeling height–diameter relationship for Populus euphratica in the Tarim riparian forest ecosystem,Northwest China

Modeling height–diameter relationships is an important component in estimating and predicting forest development under different forest management scenarios. In this paper, ten widely used candidate height–diameter models were fitted to tree height and diameter at breast height(DBH)data for Populus euphratica Oliv. within a 100 ha permanent plots at Arghan Village in the lower reaches of the Tarim River, Xinjiang Uyghur Autonomous Region of China. Data from 4781 trees were used and split randomly into two sets:75 % of the data were used to estimate model parameters(model calibration), and the remaining data(25 %) were reserved for model validation. All model performances were evaluated and compared by means of multiple model performance criteria such as asymptotic t-statistics of model parameters, standardized residuals against predicted height,root mean square error(RMSE), Akaike's informationcriterion(AIC), mean prediction error(ME) and mean absolute error(MAE). The estimated parameter a for model(6) was not statistically significant at a level of a = 0.05. RMSE and AIC test result for all models showed that exponential models(1),(2),(3) and(4) performed significantly better than others. All ten models had very small MEs and MAEs. Nearly all models underestimated tree heights except for model(6). Comparing the MEs and MAEs of models, model(1) produced smaller MEs(0.0059) and MAEs(1.3754) than other models. To assess the predictive performance of models, we also calculated MEs by dividing the model validation data set into 10-cm DBH classes. This suggested that all models were likely to create higher mean prediction errors for tree DBH classes[20 cm. However, no clear trend was found among models.Model(6) generated significantly smaller mean prediction errors across all tree DBH classes. Considering all the aforementioned criteria, model(1): TH ? 1:3 t a= e1 t b?eàc?DBHT and model(6): TH ? 1:3 t DBH2= ea t b?DBH t c ? DBH2T are recommended as suitable models for describing the height–diameter relationship of P. euphratica. The limitations of other models showing poor performance in predicting tree height are discussed. We provide explanations for these shortcomings.     

Modeling of the height–diameter relationship using an allometric equation model:a case study of stands of Phyllostachys edulis

Understanding the relationship between tree height(H) and diameter at breast height(D) is vital to forest design, monitoring and biomass estimation. We developed an allometric equation model and tested its applicability for unevenly aged stands of moso bamboo forest at a regional scale. Field data were collected for 21 plots. Based on these data, we identified two strong power relationships: a correlation between the mean bamboo height(Hm) and the upper mean H(Hu), and a correlation between the mean D(Dm) and the upper mean D(Du). Simulation results derived from the allometric equation model were in good agreement with observed culms derived from the field data for the 21 stands,with a root-mean-square error and relative root-mean-square error of 1.40 m and 13.41 %, respectively. These results demonstrate that the allometric equation model had a strong predictive power in the unevenly aged stands at a regional scale. In addition, the estimated average height–diameter(H–D) model for South Anhui Province was used to predict H for the same type of bamboo in Hunan Province based on the measured D, and the results were highly similar. The allometric equation model has multiple uses at the regional scale, including the evaluation of the variation in the H–D relationship among regions. The model describes the average H–D relationship without considering the effects caused by variation in site conditions, tree density and other factors.     

GROWTH AND YIELD MODELS FOR DAHURIAN LARCH PLANTATIONS

Growth and yield models were developed for individual tress and stands based on336 temporary plots with 405 stem analysis trees of dahurian larch(Larix gmelinii(Rupr.)Rupr.)plantations throughout Daxing’anling mountains.Several equations were selected using nonlinearregression analysis.Results showed that the Richards equation was the best model for estimatingtree height,stand mean helght and stand dominant height from age; The Power equation was thebest model for prediction tree volume from DBH and tree height; The logarithmic stand volumeequation was good for predicting stand volume from age,mean height,basal area and other standvariables.These models can be used to construct the volume table, the site index table and other for-estry tables for dahurian larch plantations.     

Allometric relationship for estimating above-ground biomass of Aegialitis rotundifolia Roxb. of Sundarbans mangrove forest, in Bangladesh

Tree biomass plays a key role in sustainable management by providing different aspects of ecosystem. Estimation of above ground biomass by non-destructive means requires the development of allometric equations. Most researchers used DBH (diameter at breast height) and TH (total height) to develop allometric equation for a tree. Very few species-specific allometric equations are currently available for shrubs to estimate of biomass from measured plant attributes. Therefore, we used some of readily measurable variables to develop allometric equations such as girth at collar-height (GCH) and height of girth measuring point (GMH) with total height (TH) for A. rotundifolia, a mangrove species of Sundarbans of Bangladesh, as it is too dwarf to take DBH and too irregular in base to take Girth at a fixed height. Linear, non-linear and logarithmic regression techniques were tried to determine the best regression model to estimate the above-ground biomass of stem, branch and leaf. A total of 186 regression equations were generated from the combination of independent variables. Best fit regression equations were determined by examining co-efficient of determination (R2), co-efficient of variation (CV), mean-square of the error (MSerror), residual mean error (Rsme), and F-value. Multiple linear regression models showed more efficient over other types of regression equation. The performance of regression equations was increased by inclusion of GMH as an independent variable along with total height and GCH.     

Individual-tree diameter growth model for Korean pine plantations based on optimized interpolation of meteorological variables

To explore the influence of meteorological variables on the growth of Korean pine(Pinus koraiensis Sieb.et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine,three approaches to interpolate meteorological variables during the growing season(i.e.,May-September) were compared in Heilongjiang Province,China.Optimized meteorological variable interpolation results were then combined with stand and individual tree variables,based on data from 56 sample plots and 2886 sample trees from Korean pine plantations in two regions of the province to develop an individualtree diameter growth model(Model I) and an individualtree diameter growth model with meteorological variables(Model Ⅱ) using a stepwise regression method.Moreover,an individual-tree diameter growth model with regional effects(Model Ⅲ) was developed using dummy variables in the regression,and the significance of introducing these dummy variables was verified with an F-test statistical analysis.The models were validated using an independent data set,and the predictive performance of the three models was assessed via the adjusted coefficient of determination(R2) and root mean square error(RMSE).The results suggest that the growth increment in tree diameter of Korean pine plantations was significantly correlated with the natural logarithm of initial diameter(ln D),stand basal area(BAS),logarithmic deformation of the stand density index(ln SDI),ratio of basal area of trees larger than the subject tree to their initial diameter at breast height(DBH)(BAL/D),and the maximum growingseason precipitation(Pgmax).The individual-tree diameter growth models of Korean pine plantations developed in this study will provide a good basis for estimating and predicting growth increments of Korean pine forests over larger areas.     

Empirical evaluation of confidence and prediction intervals for spatial models of forest structure in Jalisco,Mexico

In recent years there has been an increasing interest in developing spatial statistical models for data sets that are seemingly spatially independent.This lack of spatial structure makes it difficult,if not impossible to use optimal predictors such as ordinary kriging for modeling the spatial variability in the data.In many instances,the data still contain a wealth of information that could be used to gain flexibility and precision in estimation.In this paper we propose using a combination of regression analysis to describe the large-scale spatial variability in a set of survey data and a tree-based stratification design to enhance the estimation process of the small-scale spatial variability.With this approach,sample units(i.e.,pixel of a satellite image) are classified with respect to predictions of error attributes into homogeneous classes,and the classes are then used as strata in the stratified analysis.Independent variables used as a basis of stratification included terrain data and satellite imagery.A decision rule was used to identify a tree size that minimized the error in estimating the variance of the mean response and prediction uncertainties at new spatial locations.This approach was applied to a set of n=937 forested plots from a state-wide inventory conducted in 2006 in the Mexican State of Jalisco.The final models accounted for 62% to 82% of the variability observed in canopy closure(%),basal area(m2·ha-1),cubic volumes(m3·ha-1) and biomass(t·ha-1) on the sample plots.The spatial models provided unbiased estimates and when averaged over all sample units in the population,estimates of forest structure were very close to those obtained using classical estimates based on the sampling strategy used in the state-wide inventory.The spatial models also provided unbiased estimates of model variances leading to confidence and prediction coverage rates close to the 0.95 nominal rate.     

A new model for predicting the total tree height for stems cut-to-length by harvesters in Pinus radiata plantations

A new model for predicting the total tree height for harvested stems from cut-to-length(CTL) harvester data was constructed for Pinus radiata(D.Don) following a con?ceptual analysis of relative stem profiles,comparisons of candidate models forms and extensive selections of predictor variables.Stem profiles of more than 3000 trees in a taper data set were each processed 6 times through simulated log cutting to generate the data required for this purpose.The CTL simulations not only mimicked but also covered the full range of cutting patterns of nearly 0.45 × 10~6 stems harvested during both thinning and harvesting operations.The single-equation model was estimated through the multipleequation generalized method of moments estimator to obtain efficient and consistent parameter estimates in the presence of error correlation and heteroscedasticity that were inherent to the systematic structure of the data.The predictive performances of our new model in its linear and nonlinear form were evaluated through a leave-one-tree-out cross validation process and compared against that of the only such existing model.The evaluations and comparisons were made through benchmarking statistics both globally over the entire data space and locally within specific subdivisions of the data space.These statistics indicated that the nonlinear form of our model was the best and its linear form ranked second.The prediction accuracy of our nonlinear model improved when the total log length represented more than 20% of the total tree height.The poorer performance of the existing model was partly attributed to the high degree of multicollinearity among its predictor variables,which led to highly variable and unstable parameter estimates.Our new model will facilitate and widen the utilization of harvester data far beyond the current limited use for monitoring and reporting log productions in P.radiata plantations.It will also facilitate the estimation of bark thickness and help make harvester data a potential source of taper data to reduce the intensity and cost of the conventional destructive taper sampling in the field.Although developed for P.radiata,the mathematical form of our new model will be applicable to other tree species for which CTL harvester data are routinely captured during thinning and harvesting operations.     

Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr Type Ⅻ distributionOA

Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL) stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don) through the th...     

Mixed-effects modeling for tree height prediction models of Oriental beech in the Hyrcanian forests

Height–diameter relationships are essential elements of forest assessment and modeling efforts.In this work,two linear and eighteen nonlinear height–diameter equations were evaluated to find a local model for Oriental beech(Fagus orientalis Lipsky) in the Hyrcanian Forest in Iran.The predictive performance of these models was first assessed by different evaluation criteria: adjusted R~2(R~2_(adj)),root mean square error(RMSE),relative RMSE(%RMSE),bias,and relative bias(%bias) criteria.The best model was selected for use as the base mixed-effects model.Random parameters for test plots were estimated with different tree selection options.Results show that the Chapman–Richards model had better predictive ability in terms of adj R~2(0.81),RMSE(3.7 m),%RMSE(12.9),bias(0.8),%Bias(2.79) than the other models.Furthermore,the calibration response,based on a selection of four trees from the sample plots,resulted in a reduction percentage for bias and RMSE of about 1.6–2.7%.Our results indicate that the calibrated model produced the most accurate results.     

Spatial analysis increases efficiency of progeny testing of Chinese fir

We used spatial, global trend and post-blocking analysis to examine the effectiveness of a progeny trial in a tree breeding program for Chinese fir(Cunninghamia lanceolata(Lamb.) Hook) on a hilly site with an environmental gradient from hill top to bottom. Diameter at breast height(DBH) and tree height data had significant spatial auto-correlations among rows and columns. Adding a firstorder separable autoregressive term more effectively modelled the spatial variation than did the incomplete block(IB)model used for the experimental design. The spatial model also accounted for effects of experimental design factors and greatly reduced residual variances. The spatial analysis relative to the IB analysis improved estimation of genetic parameters with the residual variance reduced 13 and 19%for DBH and tree height, respectively; heritability increased35 and 51% for DBH and tree height, respectively; and genetic gain improved 3–5%. Fitting global trend and postblocking did not improve the analyses under IB model. The use of a spatial model or combined with a design model is recommended for forest genetic trials, particularly with global trend and local spatial variation of hilly sites.     

Variation,inheritance and correlation of growth characteristics of <Emphasis Type="Italic">Populus deltoides</Emphasis> Bartr. at various ages in the central-plain region of Punjab,India

The growth performance of twenty poplar(Populus deltoides Bartr.) clones,planted in the central-plain region of Punjab in north-western India,was evaluated using a randomized block design with three replications and plot size of four plants.Significant differences among clones were observed for diameter at breast height(DBH),height and volume per tree at age five,six and eight years.Clone L-48/89 recorded significantly superior volume than the control(G-48) at all ages,with superiority of 51.4,43.9 and 48.5 per cent at age five,six and eight years,respectively.The phenotypic and genotypic coefficients of variation were the highest for volume(26.55-34.66% and 15.84-26.00%) and the minimum for tree height(8.43-12.13% and 4.71-7.59%).The broad sense heritability was relatively higher for DBH(0.42-0.55) and genetic advance as per cent of mean was highest for volume(19.48-40.18).All genetic parameters increased with age.All traits showed significant positive correlation with each other.     

Modeling surface fuels moisture content in Pinus brutia stands

Fuel moisture content is an important variable for forest fires because it affects fuel ignition and fire behavior. In order to accurately predict fuel ignition potential, fuel moisture content must be assessed by evaluating fire spread, fireline intensity and fuel consumption.Our objective here is to model moisture content of surface fuels in normally stocked Calabrian pine(Pinus brutia Ten.) stands in relation to weather conditions, namely temperature, relative humidity, and wind speed in the Mugla province of Turkey. All surface fuels were categorized according to diameter classes and fuel types. Six fuel categories were defined: these were 0–0.3, 0.3–0.6, and0.6–1 cm diameter classes, and cone, surface litter, and duff. Plastic containers 15 9 20 cm in size with 1 9 1 mm mesh size were used. Samples were taken from 09:00 to19:00 h and weighed every 2 h with 0.01 g precision for10 days in August. At the end of the study, samples were taken to the laboratory, oven-dried at 105 °C for 24 h and weighed to obtain fuel-moisture contents. Weather measurements were taken from a fully automated weather station set up at the study site prior to the study. Correlation and regression analyses were carried out and models were developed to predict fuel moisture contents for desorption and adsorption phase for each fuel type categories. Practical fuel moisture prediction models were developed for dry period. Models were developed that performed well with reasonable accuracy, explaining up to 92 and 95.6%of the variability in fuel-moisture contents for desorption and adsorption phases, respectively. Validation of the models were conducted using an independent data set and known fuel moisture prediction models. The predictive power of the models was satisfactory with mean absolute error values being 1.48 and 1.02 for desorption and adsorption as compared to the 2.05 and 1.60 values for the Van Wagner's hourly litter moisture content prediction model. Results obtained in this study will be invaluable for fire management planning and modeling.     

Variation analysis of growth traits of four poplar clones under different water and fertilizer management

To determine appropriate quantities of water and fertilizer required for early growth of hybrid poplar cuttings,we recorded the growth traits of four clones grown under four factors(irrigation and nitrogen,phosphorus,and potassium fertilizers),each with four levels,using an orthogonal experimental design.A logistic model was used to estimate growth in height.The growth curves for tree height were sigmoid,and the model R^2 values were greater than 0.9,which indicated that the fit was highly significant.ANOVA results for tree height and basal diameter indicated that all sources of variance showed significant differences(p<0.001).The average tree height and basal diameter for all the four clones under the different treatments ranged from 155.39 to 235.04 cm,and from 13.71 to 17.42 mm,respectively.A highly positive correlation between the extreme k value and tree height was observed,suggesting that the k value was an accurate estimation of tree height.For model parameters,the earliest average time point for the onset of the rapid growth period of poplar clones was 131 d,and the highest average increment in tree height during the rapid growth period was 138.78 cm.The highest average tree height for all clones under each factor was 219,210.51,200,and 201 cm when treated with either 1200 mL of water applied every third day,3 g of nitrogen,0 g of phosphorus,or 0 g of potassium,respectively.The most suitable treatment for the early growth of hybrid poplar cuttings,as suggested by the developed logistic model,was 1200 mL of water applied every third day and three applications of 1 g nitrogen(in the form of CH4N2O).     

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.     

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.     

Site index for teak in Colombia

Determination of site quality is a basic tool for proper selection of locations and species, in management of forest plantations.Throughout the Caribbean studies of site quality are few and are hampered by statistical limitations, inappropriate growth models, and limited data. We fitted growth curves for dominant height to evaluate and classify site quality of teak (Tectona grandis) plantations by using data from 44 permanent sample plots established since 1990 in 3 22 years old teak plantations in the Colombian Caribbean region. We used Korf’s and von Bertalanffy’s models to fit curves as nonlinear effects models. Both models, with a single random parameter, were considered as adequate for dominant height growth modelling, but Korf’s model was superior. There sulting curves were anamorphic and closely reflected high variability insite quality. Five site classes were clarified: at a base age of 12 years old,teak reached a mean dominant height of 24.8 m on the best sites, 9.8 m inthe worst sites, and in the averages sites, 15.8-18.8 m. Using this model,we identified the best and the worst sites for teak plantations in the Caribbean region. This model proved a useful tool, not only for site quality evaluation, but also for improved teak plantation planning and management.     

Development of ecoregion-based merchantable volume systems for Pinus brutia Ten. and Pinus nigra Arnold. in southern Turkey

Estimating individual tree volume is one of the essential building blocks in forest growth and yield models.Ecologically based taper equations provide accurate volume predictions and allow classification by merchantable sizes, assisting in sustainable forest management.In the present study, ecoregion-based compatible volume systems for brutian pine and black pine in the three ecoregions of southern Turkey were developed. Several well-known taper functions were evaluated. A secondorder continuous-time autoregressive error structure was used to correct the inherent autocorrelation in the hierarchical data, allowing the model to be applied to irregularly spaced and unbalanced data. The compatible segmented model of Fang et al.(For Sci 46:1–12, 2000) best described the experimental data. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the three ecoregions and two species analyzed. The nonlinearextra sum of squares method indicated differences in ecoregion and tree-specific taper functions. A different taper function should therefore be used for each pine species and ecoregion in southern Turkey. Using ecoregionspecific taper equations allows making more robust estimations and, therefore, will enhance the accuracy of diameter at different heights and volume predictions.     

Vegetation structure and regeneration status of the moist,evergreen, afromontane Bore–Anferara–Wadera forest in southern Ethiopia

In a survey of the Bore–Anferara–Wadera forest to study the vegetation structure and regeneration status of woody plant species, 112 quadrats were systematically sampled along altitudinal transects to collect vegetation data. Nested sample plots of 30 m × 30 m and 5 m × 5 m were laid for collecting data on abundance and some variables of tree and shrub size. The regeneration status of woody species was assessed by counting all seedlings within the main sample plot. Woody plant species taller than or equal to 3 m were counted and their height and DBH measured. Density, frequency, basal area and importance value(IV) of woody plant species were computed. A total of 136 vascular plant species belonging to119 genera and 63 families were recorded. The overall Shannon—Wiener diversity value was 3.84 and evenness was 0.78. Total density of trees and shrubs with DBH >2 cm was 1047 ha-1. Size class distribution of woody species across different DBH and height classes indicated a relatively high proportion of individuals at lower classes,suggesting impacts of past anthropogenic disturbances.Analysis of population structure and regeneration status of the forest revealed various patterns of population dynamics where some species were represented by only a few mature plants, suggesting that they are on the verge of local extinction and that immediate conservation measures should be taken. The results highlight the need for joint management and conservation measures by the government, local people and other stakeholders to abate the rapid rate of deforestation and promote sustainable utilization of the forest resources in this forest in southern Ethiopia.     

Models and form factors for stand volume estimation in natural forest ecosystems: a case study of Katarniaghat Wildlife Sanctuary (KGWS), Bahraich District, India

In view of the difficulties in stand volume estimation in natural forests, we derived real form factors and models for volume estimation in these types of forest ecosystems, using Katarniaghat Wildlife Sanctuary as a case study. Tree growth data were obtained for all trees (dbh >10 cm) in 4 plots (25 × 25 m) randomly located in each of three strata selected in the forest. The form factor calculated for the stand was 0.42 and a range of 0.42 0.57 was estimated for selected species (density >10). The parameters of model variables were consistent with general growth trends of trees and each was statistically significant. There was no significant difference (p>0.05) between the observed and predicted volumes for all models and there was very high correlation between observed and predicted volumes. The output of the performance statistics and the logical signs of the regression coefficients of the models demonstrated that they are useful for volume estimation with minimal error. Plotting the biases with respect to considerable regressor variables showed no meaningful and evident trend of bias values along with the independent variables. This showed that the models did not violate regression assumptions and there were no heteroscedacity or multiculnarity problems. We recommend use of the form factors and models in this ecosystem and in similar ones for stand and tree volume estimation.     

Modeling frequency distributions of tree height,diameter and crown area by six probability functions for open forests of <Emphasis Type="Italic">Quercus persica</Emphasis> in Iran

The prediction of the distribution of quantitative variables in a forest stand is of great interest to forest managers, for the evaluation of forest resources and scheduling of future silvicultural treatments. The aim of this research was to model the distribution of quantitative variables for Quercus persica in open forests in Iran. To investigate the probability distribution of trees in natural stands, 642 trees were selected for measurement using a systematic random sampling method. Selected trees were measured and data were analyzed. Gamma, beta, normal,lognormal, exponential and Weibull probability distributions were fitted to the height distribution of trees. Variables of distribution functions were estimated using the maximum likelihood estimation method. Actual probability and probability which derived from functions was compared using Kolmogorov–Smirnov and Anderson–Darling tests. Beta, Weibull and Weibull probability distributions explained the distributions of tree height, DBH and crown area.