Diameter distribution model development of tropical hybrid Eucalyptus clonal plantations in Sumatera, Indonesia: A comparison of estimation methods

Background: Effective forest management and planning often requires information about the distribution of volume by size and product classes. Size-class models describe the diameter distribution and provide information by diameter class, such as the number of trees, basal area, and volume per unit of area. A successful diameter-distribution model requires high flexibility yet robust prediction of its parameters. To our knowledge, there are no studies regarding diameter distribution models for Eucalyptus hybrids in Indonesia. Therefore, the aim of this study was to compare different recovery methods for predicting parameters of the 3-parameter Weibull distribution for characterising diameter distributions of Eucalyptus hybrid clone plantations, on Sumatera Island of Indonesia. Methods: The parameter recovery approach was proposed to be compatible with stand-average growth and yield models developed based on the same data. Three approaches where compared: moment-based recovery, percentile-based prediction and hybrid methods. The ultimate goal was to recover Weibull parameters from future stand attributes, which were predicted from current stand attributes using regression models. Results: In this study, the moment method was found to give the overall lowest mean error-index and Kolmogorov– Smirnov (KS) statistic, followed by the hybrid and percentile methods. The moment-based method better fit long tails on both sides of the distribution and exhibited slightly greater flexibility in describing plots with larger variance than the other methods. Conclusions: The Weibull approach appeared relatively robust in determining diameter distributions of Eucalyptus hybrid clone plantation in Indonesia, yet some refinements may be necessary to characterize more complex distributions.

Predicting parameters of Weibull probability density function for diametric distributions in A. melanoxylon, E. camaldulensis, and E. nitens bioenergy plantation

Precise modeling of stand diameter distributions is required to provide accurate estimates of volume per diameter class and unit area. Therefore, it is necessary to obtain the most accurate probability density functions parameters estimates to predict stand diameter distribution in time. We evaluate two methods to estimate the parameters of the Weibull probability density function in the modeling of diameter distributions of bioenergy plantations. The methods considered a direct method of parameter prediction based on regression models (PPRM) and an indirect method of parameter recovery through the determination of percentiles (PRDP). Both methods are considered systems of linear equations and are adjusted through simultaneous estimation of parameters using stand variables. The greatest precision was obtained with PPRM. The PRDP method was not effective in the prediction of diameter distributions due to the high level of truncation of the observed distributions showing an overestimation of the distribution for the largest diameter classes. Estimated parameters of the Weibull PDF are directly related to mean height, quadratic mean diameter, and crop age; and are inversely related to stocking.

A distribution-centered approach for analyzing human adipocyte size estimates and their association with obesity-related traits and mitochondrial function

Objective Cell diameter, area, and volume are established quantitative measures of adipocyte size. However, these different adipocyte sizing parameters have not yet been directly compared regarding their distributions. Therefore, the study aimed to investigate how these adipocyte size measures differ in their distribution and assessed their correlation with anthropometry and laboratory chemistry. In addition, we were interested to investigate the relationship between fat cell size and adipocyte mitochondrial respiratory chain capacity. Methods Subcutaneous and visceral histology-based adipocyte size estimates from 188 individuals were analyzed by applying a panel of parameters to describe the underlying cell population. Histology-based adipocyte diameter distributions were compared with adipocyte diameter distributions from collagenase digestion. Associations of mean adipocyte size with body mass index (BMI), glucose, HbA1C, blood lipids as well as mature adipocyte mitochondrial respiration were investigated. Results All adipocyte area estimates derived from adipose tissue histology were not normally distributed, but rather characterized by positive skewness. The shape of the size distribution depends on the adipocyte sizing parameter and on the method used to determine adipocyte size. Despite different distribution shapes histology-derived adipocyte area, diameter, volume, and surface area consistently showed positive correlations with BMI. Furthermore, associations between adipocyte sizing parameters and glucose, HbA1C, or HDL specifically in the visceral adipose depot were revealed. Increasing subcutaneous adipocyte diameter was negatively correlated with adipocyte mitochondrial respiration. Conclusions Despite different underlying size distributions, the correlation with obesity-related traits was consistent across adipocyte sizing parameters. Decreased mitochondrial respiratory capacity with increasing subcutaneous adipocyte diameter could display a novel link between adipocyte hypertrophy and adipose tissue function.

Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

Long-Term Trends of Planted Loblolly Pine Diameter Distribution Characteristics

Diameter distributions are fundamental characteristics of stand structure. It is widely assumed that unthinned plantation loblolly pine (Pinus taeda L.) diameter distributions are unimodal and slightly skewed. In this work, the assumption of unimodality is formally tested and confirmed using 413 long-term permanent plots representing three generations of genetics and silviculture across the native range of loblolly pine in the southeastern United States. Approximately 96% of plot measurements had no significant evidence to reject the hypothesis of unimodality. While levels often significantly differed, similar developmental trends of skewness, kurtosis, and estimated Weibull parameters were observed despite the advances of genetics and silviculture. The results of the study indicate the continued need for a flexible distribution for characterizing diameter distributions in plantation loblolly pine. Study Implications Knowledge of diameter distribution helps inform management activities. Further, assessing monetary or ecological value requires an understanding of a stand’s diameter structure. Using three long-term research studies established across the native range of the loblolly pine, this investigation confirms the assumption of slightly skewed, unimodal distributions. Additionally, long-term trends in skewness, kurtosis, and fitted Weibull parameters across the three generations of genetics and silviculture represented in the studies are presented. The results of this work confirm the need for a flexible distribution model form and indicate that managers can expect similar trends in diameter distribution structure in both vintage and contemporary stands at least until first thinning.

Modelling the Diameter Distribution of Savanna Trees with Drone-Based LiDAR

The diameter distribution of savanna tree populations is a valuable indicator of savanna health because changes in the number and size of trees can signal a shift from savanna to grassland or forest. Savanna diameter distributions have traditionally been monitored with forestry techniques, where stem diameter at breast height (DBH) is measured in the field within defined sub-hectare plots. However, because the spatial scale of these plots is often misaligned with the scale of variability in tree populations, there is a need for techniques that can scale-up diameter distribution surveys. Dense point clouds collected from uncrewed aerial vehicle laser scanners (UAV-LS), also known as drone-based LiDAR (Light Detection and Ranging), can be segmented into individual tree crowns then related to stem diameter with the application of allometric scaling equations. Here, we sought to test the potential of UAV-LS tree segmentation and allometric scaling to model the diameter distributions of savanna trees. We collected both UAV-LS and field-survey data from five one-hectare savanna woodland plots in northern Australia, which were divided into two calibration and three validation plots. Within the two calibration plots, allometric scaling equations were developed by linking field-surveyed DBH to the tree metrics of manually delineated tree crowns, where the best performing model had a bias of 1.8% and the relatively high RMSE of 39.2%. A segmentation algorithm was then applied to segment individual tree crowns from UAV-LS derived point clouds, and individual tree level segmentation accuracy was assessed against the manually delineated crowns. 47% of crowns were accurately segmented within the calibration plots and 68% within the validation plots. Using the site-specific allometry, DBH was modelled from crown metrics within all five plots, and these modelled results were compared to field-surveyed diameter distributions. In all plots, there were significant differences between field-surveyed and UAV-LS modelled diameter distributions, which became similar at two of the plots when smaller trees (<10 cm DBH) were excluded. Although the modelled diameter distributions followed the overall trend of field surveys, the non-significant result demonstrates a need for the adoption of remotely detectable proxies of tree size which could replace DBH, as well as more accurate tree detection and segmentation methods for savanna ecosystems.

PECULIARITIES OF THE DIAMETER DISTRIBUTIONS OBTAINED AT SUBMILISECOND DURATION OF DISCHARGE PULSES SPARK-EROSIVE ALUMINUM PARTICLES AND CAVERNS ON THE SURFACE OF ITS GRANULES

The conditions and technique for obtaining single-mode size distributions of spark-erosive aluminum particles are given. The statistical parameters of the size distributions of spark-erosive aluminum particles and caverns on the surface of its granules, obtained at a submilisecond duration of discharge pulses were calculated. A comparative analysis of the volumes of metal of erosion caverns and particles is carried out. The agreement of the diameter distributions of spark-erosive particles and caverns obtained in practice with the following theoretical distributions of a continuous random variable: Gauss, Weibull, the integral of the Rosin-Rammler function, and also log-normal distribution is verified. In this case, the parameters of theoretical distributions were calculated both by the statistical parameters of the distributions obtained in practice, and by the criterion of the smallest value of the average module of the relative deviation of the theoretical and practical distributions. It has been shown that for the values of the parameters of theoretical distributions that correspond to the statistical parameters of practical distributions, the distribution of erosive particles by diameters is in the best agreement with the Gauss distribution, and the caverns – with the distribution of integral of the Rosin-Rammler function. References 27, figures 2, tables 3.