Search Results (17)

The accurate assessment of tree volume is crucial for developing forest management plans, and this can be achieved using tree volume models. In this study, data on individual trees were collected and calculated, including the diameter at breast height (D), ground diameter (DG), tree height (H), and tree volume (V). A total of 400 Populus × tomentosa Carrière, 400 Populus tomentosa Carr, and 400 Populus × canadensis Moench trees were sampled. Two compatible volume model systems were established using corresponding methods. The models consisted of the following five types: V-DH, V-D, V-DG, H-D, and DG-D. In our calculations, before the horizontal line was the dependent variable, and behind the horizontal line was the independent variable. Variations in preferences for the H-D models were observed among the tree species, with the logistic function proving the most suitable for Populus × tomentosa Carrière, Chapman–Richard function for Populus tomentosa Carr, and power function for Populus × canadensis Moench. Among the three volume models, the V-DH model exhibited a superior performance, with its R² values ranging from 0.965 to 0.984 and mean estimated error (MPE) values ranging from 1.26% to 1.78%. Following this was the V-D model, with R² values between 0.9359 and 0.9704 and MPE values between 1.71% and 2.46%. The V-DG model ranked third, with R² values ranging from 0.8746 to 0.9501 and MPE values ranging from 2.33% to 3.16%. In the H-D model, the R² and MPE values ranged from 0.4998 to 0.7851 and from 1.31% to 1.45%, respectively. For the DG-D model, the R² values ranged from 0.9563 to 0.9868 and the MPE values ranged from 0.47% to 0.68%. Comparing both compatible methods, the nonlinear seemingly uncorrelated regression (NSUR) was more effective. The three volume models demonstrated high levels of accuracy and compatibility, providing a reliable scientific foundation for forest management and the formulation of harvesting plans in Beijing, with significant practical implications. Full article

In this study, the biomass expansion factor (BEF) method was combined with the tree growth function in order to obtain a more accurate growth function of tree species through the fitting of different growth functions to tree growth, and to determine the characteristics of the forest carbon stock as well as the carbon sink potential of Huangshan National Forest Park (HNFP) in China. The carbon sink potential of each tree species and the integrated influencing factors, such as the stand and soil, were directly represented by structural equation modelling (SEM) to clarify the size and path of each influencing factor against the carbon sink potential. The results showed the following: (1) the logistic growth function fitting results for the seven major tree species in HNFP were better than those from the Richard–Chapman growth function, and the R² was greater than 0.90. (2) In 2014, the total carbon stock of the forest in HNFP was approximately 9.59 × 10⁵ t, and the pattern of carbon density, in general, was higher in the central region and the northeastern region and lower in the northern and southern regions, while the distribution of carbon density was lower in the northern and southern regions. The carbon density pattern generally showed a higher distribution in the central and northeastern regions and a lower distribution in the northern and southern regions; most of the high-carbon-density areas were distributed in blocks, while the low-carbon-density areas were distributed sporadically. (3) The total carbon sink of the forest in HNFP was 8.26 × 10³ t in 2014–2015, and due to the large age structure of the regional tree species, the carbon sinks of each tree species and the total carbon sink of HNFP showed a projected downward trend from 2014 to 2060. (4) For different tree species, the influencing factors on carbon sink potential are not the same, and the main influence factors involve slope position, slope, altitude, soil thickness, etc. This study identified the carbon stock and carbon sink values of the forest in HNFP, and the factors affecting the carbon sink potential obtained by SEM can provide a basis for the selection of new afforestation sites in the region as well as new ideas and methods to achieve peak carbon and carbon neutrality both regionally and nationally in the future. Full article

To model dynamic systems in various situations results in an ordinary differential equation of the form ${\displaystyle \frac{dy}{dt}}=g(y,t,\theta )$, where g denotes a function and $\theta$ stands for a parameter or vector of unknown parameters that require estimation from observations. In order to consider environmental fluctuations and numerous uncontrollable factors, such as those found in forestry, a stochastic noise process ${ϵ}_t$ may be added to the aforementioned equation. Thus, a stochastic differential equation is obtained: ${\displaystyle \frac{d{Y}_t}{dt}}=f(Y_t,t,\theta )+{ϵ}_t$. This paper introduces a method and procedure for parameter estimation in a stochastic differential equation utilising the Richards model, facilitating growth prediction in a forest’s tree population. The fundamental concept of the approach involves assuming that a deterministic differential equation controls the development of a forest stand, and that randomness comes into play at the moment of observation. The technique is utilised in conjunction with the logistic model to examine the progression of an agricultural epidemic induced by a virus. As an alternative estimation method, we present the Random Time Transformation (RTT) method. Thus, this paper’s primary contribution is the application of the RTT method to estimate the Richards model, which has not been conducted previously. The literature often uses the logistic or Gompertz models due to difficulties in estimating the parameter form of the Richards model. Lastly, we assess the effectiveness of the RTT Method applied to the Chapman–Richards model using both simulated and real-life data. Full article

Competition among free branches in the tree canopy is an important factor influencing branch length growth. Therefore, there is a need to quantify this competition and to understand the impact of the regression technique on the predictive accuracy of the growth of free branch length (GFBL) model in a Larix principis-rupprechtii plantation. This study focused on an L. principis-rupprechtii plantation in Saihanba Mechanized Forest Farm. Five competition indices based on 2176-branch data points from 76 trees were used to quantify the branch competition, and three regression techniques (nonlinear least squares (NLS), nonlinear mixed-effects model (NLME), and nonlinear quantile regression (NQR)) were used to construct the GFBL model including the branch competition index. The results showed that the Chapman–Richards growth function, including the diameter at breast height (DBH) and depth of branch into crown (DINC), was the optimal equation for describing the GFBL in the studied L. principis-rupprechtii plantation. The branch competition index (CI) was found to be optimal for quantifying the branch competition when used with the maximum value parameter (${\mathrm{a}}_0$) of the Chapman–Richards growth function. The three parameter estimation methods were compared, and the NLME, which included the CI, was found to have the highest predictive accuracy. The results of this study can act as a reference for improving the management, assessing the management effectiveness, and enhancing the quality of L. principis-rupprechtii plantations. Full article

Laurel (Cordia alliodora Ruiz & Pav. Oken) is a Neotropical native tree that is easily regenerated in the secondary forest within the Amazon region. Amazonian smallholders use this tree regeneration to obtain a homogeneous forest cover when developing local agroforestry systems, which do not depend on nursery seedling production for tree planting. The objective of the present investigation was to develop growth and yield models for Laurel within the local agroforestry systems. A total of 226 sampling plots were measured between 2010–2011 and 2014–2015. Chapman- Richard, Hosslfeld II, and the generalized algebraic difference approach (GADA) form of the Chapman-Richard’s function was used for modeling height-age and diameter-age relationships. Eight volume models were tested to describe total stem volume. The GADA method was suited to describe the Laurel height and diameter-age growth. The cutting cycle for agroforestry systems with a density of 300 trees ha⁻¹ at the best site index (SI) (22 m) produced 13.9 m³ ha⁻¹ year⁻¹ and a total wood yield of 195.1 m³ ha⁻¹ at age 14. In the worst SI (14 m), the average annual yield was 3.5 m³ ha⁻¹, with a total yield of 83.3 m³ ha⁻¹ at age 24 years. The Spurr potential model was the best fit to describe the volume of the Laurel according to the Akaike information criteria. The Laurel biological (optimal) rotation age suggests that the minimum cutting diameter should be lowered from 30 cm of DBH in the research zone. Management of the natural regeneration of secondary forests by smallholders is a local agroforestry practice that should be given greater attention, especially within protected forest areas. Full article

To study the deformation characteristics of crushed gangue under different water content conditions, the confined compaction test of crushed gangue was carried out under five different water content conditions by using a universal material testing machine and a compaction device. The strain–stress relationship in the compaction process of crushed gangue and the crushing law of gangue particles were obtained through the test, and the effects of the axial stress, water content, and relative crushing rate on the compaction deformation of crushed gangue were analyzed. The results show that the confined compaction deformation process of crushed gangue can be divided into three stages: the rapid compaction stage, crushing compaction stage, and stable compaction stage. The strain–stress relationship can be described by the parameter logarithmic function and Chapman–Richards function, respectively. The maximum change in the compression modulus under different water content states ranged from 9.9 to 19.3 MPa, and the influence of the water content on the compression modulus was more significant with increasing axial stress. There is a good correlation between particle crushing and compaction deformation. The relative crushing rate increases with the increase in the axial strain, and the increasing rate of the relative crushing rate also gradually increases. The change law of the relative crushing rate and axial strain is different in dry and water-containing conditions. Full article

Tree growth in Korean red pine (Pinus densiflora, hereafter Pd), Korean white pine (Pinus koraiensis, hereafter Pk), and Japanese larch (Larix kaempferi, hereafter Lk) was modeled using Logistic, Korf, Gompertz, Chapman-Richards, and Weibull equations and stem analysis data from sample trees: 38 trees for Pd, 46 trees for Pk, and 45 trees for Lk. The models were fitted to the total increment of tree size variables, diameter at breast height (DBH), height, basal area, and stem volume, as a function of age. After selecting the best-fit growth function, the current annual increment (CAI) and mean annual increment (MAI) were compared for each variable by species. The optimal growth functions were Chapman-Richards for DBH and stem volume, Korf for height, and Gompertz for basal area. The parameter estimates in the final models were all significant (p < 0.01) with best-fit statistics and unbiased residual plots. When plotted with observed values, the growth patterns of each variable were represented properly. The predicted growth curves over age were concave with respect to the Y-axis in DBH and height but lightly convex in basal area, and explicitly convex in stem volume, whereas an asymptote of sigmoid curve in stem volume was not apparent until 100 years. Age with the maximum MAI among variables was arranged similarly to CAI; the age with maximum MAI was earliest for DBH and latest for volume. The maximum growth was achieved earliest in Lk, followed by Pk and Pd. The developed models were able to predict tree size variables and serve as a reference to understand growth characteristics by species. Full article

Tree growth models describe the growth and development of forest ecosystems by considering how the dimensions of each simulated tree change within a certain time. These models have commonly used three growth parameters that describe various biological processes and behaviours, considering a sigmoid growth function: (i) the upper asymptote (θ₁), which is the maximal yield indicated by a final dimension (such as the maximal stem diameter); (ii) the maximum specific growth rate (θ₂), defined as the slope of the tangent at the inflexion point; and (iii) the time elapsed (θ₃), defined by the intercept of this tangent with the abscissas. To the best of our knowledge, however, associations between the three parameters have not been documented for tree species. Using diameter growth data from pine trees located in typical mixed and uneven-aged pine-oak forests in the Sierra Madre Occidental, Mexico, our study aims were: (i) to quantify the putative associations between the three growth parameters and (ii) to test the accuracy of a proposed Hybrid Chapman-Richards growth model based on associations between the three growth parameters, but including only one single parameter, relative to the widely used Generalized Algebraic Difference Approach (GADA) based on the Chapman-Richards, Lundqvist and Hossfeld models and the Hybrid Weibull Model. For statistical comparison of the quality of the models, we used the mean relative percentage error, root mean square error, coefficient of determination and Akaike information criterion to assess the quality of the fit. Although the quality of the five growth models studied was similar, from a practical point of view, the proposed Hybrid Chapman-Richards Model (CR-H) is easier to apply than the other models and has a lower data collection and computational cost. The parameter of CR-H can be easily obtained, by measuring just the dominant trees, especially in coniferous forests with irregular ages. Moreover, in contrast to the Chapman-Richards-GADA factor χ₀, when θ₂ is assumed to be site-specific, the CR-H has always a closed-form solution. Full article

In the process of modeling height–diameter models for Mongolian pine (Pinus sylvestris var. mongolica), the fitting abilities of six models were compared: (1) a basic model with only diameter at breast height (D) as a predictor (BM); (2) a plot-level basic mixed-effects model (BMM); (3) quantile regression with nine quantiles based on BM (BQR); (4) a generalized model with stand or competition covariates (GM); (5) a plot-level generalized mixed-effects model (GMM); and (6) quantile regression with nine quantiles based on GM (GQR). The prediction bias of the developed models was assessed in cases of total tree height (H) predictions with calibration or without calibration. The results showed that extending the Chapman–Richards function with the dominant height and relative size of individual trees improved the prediction accuracy. Prediction accuracy was improved significantly when H predictions were calibrated for all models, among which GMM performed best because random effect calibration provided the lowest prediction bias. When at least 8% of the trees were selected from a new plot, relatively accurate and low-cost prediction results were obtained by all models. When predicting the H values of Mongolian pine for a new stand, GMM and BMM were preferable if there were available height measurements for calibration; otherwise, GQR was the best choice. Full article

The objectives of this study were to develop site index and variable-density yield models for Korean red pine (Pinus densiflora Siebold & Zucc.), Korean white pine (P. koraiensis S. & Z.), and Japanese larch (Larix kaempferi (Lamb.) Carrière) in Korea. The data were collected between 2012 and 2021 from repeatedly measured empirical plots in each target stand in the North Central region of Korea: Gangwon and North Gyeongsang provinces. To develop the site index for each species, a dominant height growth model by species was developed using the Chapman–Richards function. The site index was computed with a base age of 40 years and used as an independent variable to predict the stand volume. To develop the variable-density yield models, three stand density variables, the stand age, and the site index were applied. The stand density variables used were the stand basal area, the number of trees per hectare, and the relative density. All the models were successfully developed with significant parameters and reasonable fit statistics, and the residuals analyzed presented unbiased scatter plots. Yield models with the stand basal area, or the number of trees, can be used to predict the stand volume. The yield model with relative density was flexible to apply across the stand age because the input of the absolute stand density was not required. Model simulation and comparisons with other studies also supported the applicability of the models developed in this study. The models were found to be highly applicable for predicting and simulating these targeted stands, particularly in Korea. Full article

The breeding of Norway spruce in northern Europe has substantially contributed to the production of high-quality wood. The vegetative propagation of robust elite clones could help to sustain the provision of high-quality timber in the face of changing climates. For the adequate evaluation of genetic gains, the altered tree growth dynamics of the clones need to be understood, yet essential information about the long-term growth dynamics of improvedboreal trees is still lacking. We examined a 50-year-old clonal plantation in Latvia to distinguish the clonal effects on diameter growth function parameters and estimate the genetic parameters. A mixed-effect modelling approach was used, in which the clones were applied as random effects on the parameters of the Chapman–Richard equation. All model parameters showed significant variance in the genotypic coefficients of variation CV_g which ranged between 11.0 and 17.1%, with the highest being for the growth rate. The heritability (H²) of the diameter at breast height (DBH) reached 0.35 at the age of 40, while CV_g decreased from 12.9% to 7.8% between the ages of 20 and 45. Age–age genotypic correlations were positive and were strong or very strong (>0.76). The realised genetic gain varied from −6.3 to +24.0% around the trial mean. A substantial improvement in DBH was indicated when elite clones were selected for vegetative propagation based not only on early measurements, but also considering the genetic variance in the model parameters. Full article

Growth differences between key commercial species and between silvicultural intensities (phases) within a species in a region are of great interest to foresters. This study used modeling methods to investigate these differences in east Texas. Datasets collected from loblolly and slash pine plots installed in extensively managed plantations (Phase I) and loblolly pine plots installed in intensively managed plantations (Phase II) were used. Species and silvicultural phase growth differences were determined by comparing their height–age, diameter–age, and height–diameter relationships. Slash and loblolly pine had significantly different parameter estimates for the Chapman and Richards function-based height– and diameter–age models. Slash pine grew faster than loblolly pine, with the superiority in height increasing while that of diameter growth decreased slightly with age. Slash and loblolly pine differed also in all parameter estimates of the exponential function-based height-diameter model. Loblolly pine was taller than the slash for small size (DBH ≤ 18 cm) trees, but thereafter, slash pine outperformed loblolly. While these results may encourage planting slash pine in the region, more studies are needed before definitive conclusions can be made. The differences in the height–age models for loblolly pine Phase I and II plots suggest that intensive management significantly enhanced tree height growth. However, this enhancement did not substantially change the maximum height; instead, trees reached the maximum height younger, thus effectively shortening the rotation age. Full article

The prediction of tree growth is key to further understand the carbon sink role of forests and the short-term forest capacity on climate change mitigation. In this work, we used large-scale data available from three consecutive forest inventories in a Euro-Mediterranean region and the Bertalanffy–Chapman–Richards equation to model up to a decade’s tree size variation in monospecific forests in the growing stages. We showed that a tree-level fitting with ordinary differential equations can be used to forecast tree diameter growth across time and space as function of environmental characteristics and initial size. This modelling approximation was applied at different aggregation levels to monospecific regions with forest inventories to predict trends in aboveground tree biomass stocks. Furthermore, we showed that this model accurately forecasts tree growth temporal dynamics as a function of size and environmental conditions. Further research to provide longer term prediction forest stock dynamics in a wide variety of forests should model regeneration and mortality processes and biotic interactions. Full article

In light of the difficulties in stand volume estimation of natural forests, we analyzed height–diameter relationships and derived a set of height estimation equations for volume estimation for naturally developing forest ecosystems, using the Järvselja old-growth and the Laeva commercial forest in Estonia as a case study. This contribution presents an approach to model individual tree height–diameter relationships for Scots pine, common aspen, silver and downy birch, Norway spruce, black alder, gray alder, linden species, European ash, Norway maple, deciduous species and coniferous species in multi-size and mixed-species naturally developing stands in Estonia. Single-tree-level data were collected in 2013. Two methods were used to obtain stand-level data: whole surface inventory and partial surface inventory. To model the height–diameter relationship in naturally developed mixed-species forest stands in order to predict single tree height based on observed diameter at breast height, we applied nonlinear mixed models where we applied the Chapman–Richards and Näslund models as fixed-effects and the influence of the species contribution at the sites as random effects. The fixed-effects followed a set of criteria: (1) height starts at h = 1.3; d = 0; (2) the applied functions are monotonically increasing with a clear inflection point and 3) the fixed-effect model has an asymptotic value) in a naturally developed mixed-species forest. Full article

Traditional site index curves are frequently produced for shade-intolerant species but are scarce for shade-tolerant species. Red spruce (Picea rubens Sarg.) can be found in three distinct geographic regions (northern, central, and southern) within the Appalachian Mountains. The one commonly used set of red spruce site index curves is over ninety years old. A definite need exists for a modern, regionally applicable set of site index curves. This research sampled 83 plots randomly located in the central Appalachians of West Virginia. Three sets of anamorphic site index curves were created after careful examination of height models built using Chapman-Richards and Meyer functions. One set of curves was constructed with traditional age height pairs. The second utilized a suppression-corrected age and height pair. The third set examined diameter at breast height (DBH) and height pairs. Fit statistics indicated better performance for the suppression-corrected age–height pair site index and the DBH–height pair site index versus the traditional age–height pair models. Site index conversion equations were also investigated for the red spruce age-corrected site index. Linear regression was used to determine significant geographic and climate variables and the utility of including site index values for red maple (Acer rubrum L.) and yellow birch (Betula alleghaniensis Britton) in the model to predict red spruce site index. Significant models were found for varying combinations of species site index, climate, and geographic variables with R²_adj in the range of 0.139–0.455. These new site index curves and conversion equations should provide utility for site productivity estimation and growth and yield modeling while aiding in restoration efforts for this important central Appalachian species. Full article