A finite mixture of two Weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands

2001 ◽  
Vol 31 (9) ◽  
pp. 1654-1659 ◽  
Author(s):  
Lianjun Zhang ◽  
Jeffrey H Gove ◽  
Chuangmin Liu ◽  
William B Leak
Keyword(s):  
Model Fitting ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Diameter Distribution ◽  
Weibull Distributions ◽  
Forest Stands ◽  
Negative Exponential Function ◽  
Diameter Frequency Distribution ◽  
Negative Exponential ◽  
Diameter Distributions

The rotated-sigmoid form is a characteristic of old-growth, uneven-aged forest stands caused by past disturbances such as cutting, fire, disease, and insect attacks. The diameter frequency distribution of the rotated-sigmoid form is bimodal with the second rounded peak in the midsized classes, rather than a smooth, steeply descending, monotonic curve. In this study a finite mixture of two Weibull distributions is used to describe the diameter distributions of the rotated-sigmoid, uneven-aged forest stands. Four example stands are selected to demonstrate model fitting and comparison. Compared with a single Weibull or negative exponential function, the finite finite mixture model is the only one that fits the diameter distributions well and produces root mean square error at least four times smaller than the other two. The results show that the finite mixture distribution is a better alternative method for modeling the diameter distribution of the rotated-sigmoid, uneven-aged forest stands.

scholarly journals A percentile-based estimator for the log-logistic function: Application to forestry

2020 ◽  
Vol 72 (1) ◽  
pp. 107-120
Author(s):  
Friday Nwabueze Ogana
Keyword(s):  
Estimation Method ◽  
Tectona Grandis ◽  
Logistic Function ◽  
Growth And Yield ◽  
Estimation Methods ◽  
Diameter Distribution ◽  
Logistic Distribution ◽  
Forest Stands ◽  
Forest Modelling ◽  
Diameter Distributions

AbstractDeveloping a simplified estimation method without compromising the performance of the distribution is germane to forest modelling. Few estimation methods exist for the Log-Logistic distribution and are relatively complex. A simplified estimator for the Log-Logistic parameters will increase its application in diameter distribution yield systems. Therefore, in this study, a percentile-based estimator was applied for the Log-Logistic distribution. The Kolmogorov-Smirnov, Anderson-Darling and Cramer-von Mises statistics were used to evaluate the method in two natural forest stands and two monospecific plantations of Gmelina arborea Roxb. and Tectona grandis Linn. f. in Nigeria. The parameter recovery model (PRM) and parameter prediction model (PPM) were used to predict the diameter distributions of independent stands of G. arborea and T. grandis. The results showed that the percentile estimator did not compromise the quality of fits of the Log-Logistic function across the four forest stands and are comparable to the maximum likelihood estimator. The 25th and 75th, and 40th and 80th were the best sample percentiles for the estimator. The predicted diameter distributions of G. arborea and T. grandis stands from the PRM and PPM were reasonable and compare well with the observed distribution. Thus, either of the models can be incorporated into the growth and yield system of forest stand management.

scholarly journals PILOT STUDY ON THE RETRIEVAL OF DBH AND DIAMETER DISTRIBUTION OF DECIDUOUS FOREST STANDS USING CAST SHADOWS IN UAV-BASED ORTHOMOSAICS

2018 ◽  
Vol IV-1 ◽  
pp. 93-99 ◽  
Author(s):  
T. Kattenborn ◽  
J. Hernández ◽  
J. Lopatin ◽  
G. Kattenborn ◽  
F. E. Fassnacht
Keyword(s):  
Pilot Study ◽  
Deciduous Forest ◽  
Basal Area ◽  
Aerial Imagery ◽  
Diameter Distribution ◽  
Forest Stands ◽  
Efficient Retrieval ◽  
Difficult Terrain ◽  
Diameter Distributions

<p><strong>Abstract.</strong> One fundamental metric to characterize trees and forest stands is the diameter at breast height (DBH). However, the vertical geometry of tree stems hampers a direct measurement by means of orthographic aerial imagery. Nevertheless, the DBH in deciduous forest stands could be measured from UAV-based imagery using the width of a stem´s cast shadow projected on the ground. Here, we compare in-situ measured DBH of 100 trees with the DBH visually interpreted from cast-shadows derived in UAV-based aerial imagery. Then, based on simulated datasets, we determine suitable DBH sampling sizes for a robust and efficient retrieval of stand diameter distributions. The UAV-based DBH estimation resulted in an r<sup>2</sup> of 0.74, RMSE of 7.61<span class="thinspace"></span>cm, NRMSE of 12.8<span class="thinspace"></span>% and approximately unbiased results. According to our simulations it can be assumed that a sample size of 25&amp;ndash;50 individual DBH measurements per forest stand allows estimating reliable diameter distributions. The presented pilot study gives a first insight on the potential of such an approach for operational assessments of diameter distribution in deciduous forest stands and might be particularly interesting for stands in difficult terrain situations. The presented approach can be extended to estimate the basal area, timber stock or biomass.</p>

Estimation of the diameter distribution of a stand marked for cutting using finite mixtures

2007 ◽  
Vol 37 (4) ◽  
pp. 817-824 ◽  
Author(s):  
Klaus Nordhausen ◽  
Tapio Nummi
Keyword(s):  
Sample Size ◽  
Finite Mixture Models ◽  
Mixture Distribution ◽  
Parametric Model ◽  
Finite Mixture ◽  
Diameter Distribution ◽  
Practical Implementation ◽  
Production Potential ◽  
Component Mixture ◽  
Reasonable Choice

The aim of this paper is to find a parametric model for the diameter distribution when a sample of trees in a stand is measured by a harvester. It has important applications prior to and during harvesting for the assessment of the production potential of the stand marked for cutting. We apply the finite mixture models for tree species separately. Our data consist of six real forest stands measured in Finland. Our results showed that, for practical implementation, a three-component Lognormal mixture distribution seemed to be a reasonable choice. The subsample analysis indicated that, for certain stands, a sample size as low as 100 provides a quite good average fit for the chosen three-component mixture distribution, but for other stands, the sample size should be much larger.

A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions

2020 ◽  
Author(s):  
Adrian Norman Goodwin
Keyword(s):  
Lower Bound ◽  
Blind Spot ◽  
Forest Growth ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Absolute Difference ◽  
Weibull Function ◽  
Distribution Models ◽  
Difference Statistic ◽  
Diameter Distributions

Abstract Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

Deriving Tree Diameter Growth and Probability of Survival Equations from Successive Diameter Distributions

2008 ◽  
Vol 54 (1) ◽  
pp. 31-35
Author(s):  
Thomas G. Matney ◽  
Emily B. Schultz
Keyword(s):  
General Procedure ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Diameter Growth ◽  
Individual Tree ◽  
Statistical Probability ◽  
Growth And Survival ◽  
Tree Diameter ◽  
Growth And Yield Models ◽  
Diameter Distributions

Abstract Many growth and yield models have used statistical probability distributions to estimate the diameter distribution of a stand at any age. Equations for approximating individual tree diameter growth and survival probabilities from dbh can be derived from these models. A general procedure for determining the functions is discussed and illustrated using a loblolly pine spacing study. The results from the spacing study show that it is possible to define tree diameter growth and survival probability functions from diameter distributions with an accuracy sufficient to obtain a link between the individual tree and diameter growth and yield models.

Some observations on fitting assumed diameter distributions to horizontal point sampling data

2000 ◽  
Vol 30 (4) ◽  
pp. 521-533 ◽  
Author(s):  
Jeffrey H Gove
Keyword(s):  
Diameter Distribution ◽  
Parameter Estimates ◽  
Sample Point ◽  
Underlying Distribution ◽  
Weighted Distribution ◽  
Reliable Parameter ◽  
Simulation Results ◽  
Larger Sample ◽  
Horizontal Point Sampling ◽  
Diameter Distributions

This paper revisits the link between assumed diameter distributions arising from horizontal point samples and their unbiased stand-based representation through weighted distribution theory. Examples are presented, which show that the assumption of a common shared parameter set between these two distributional forms, while theoretically valid, may not be reasonable in many operational cases. Simulation results are presented, which relate the conformity (or lack thereof) in these estimates to sampling intensity per point and the underlying shape of the population diameter distribution from which the sample point was drawn. In general, larger sample sizes per point are required to yield reliable parameter estimates than are generally taken for inventory purposes. In addition, a complimentary finding suggests that the more positively skewed the underlying distribution, the more trees per point are required for good parameter estimates.

Selective Synthesis of Single-Walled Carbon Nanotubes by Blending Catalysts

2007 ◽  
Author(s):  
Shuhei Inoue ◽  
Takeshi Nakajima ◽  
Kazuya Nomura ◽  
Yoshihiro Kikuchi
Keyword(s):  
Carbon Nanotubes ◽  
Fermi Level ◽  
Chemical Vapor ◽  
Single Walled Carbon Nanotubes ◽  
Diameter Distribution ◽  
Efficient Catalyst ◽  
Single Walled Carbon ◽  
Similar Density ◽  
Walled Carbon Nanotubes ◽  
Diameter Distributions

Single-walled carbon nanotubes are considered the most attractive material and a lot of synthesis processes are developed. Among these synthesis processes chemical vapor deposition processes are considered to be most suitable for macroscopic production. In many CVD processes the alcohol catalytic CVD process can be the best process because it can produce very pure nanotubes without any purification. However, cobalt is essential as a catalyst that makes the flexibility of catalysts restricted. In this paper, our investigation mainly focused on as follows: The efficiency of combined catalysts with/without cobalt. The diameter distributions against catalysts density. The electrical states of catalysts near Fermi level. Consequently, almost all of cobalt containing catalysts worked well, and the diameter distributions were proportional to the particle size. Efficient catalysts had enough states around Fermi level and the cobalt-less efficient catalyst cluster model showed the similar density of state to the cobalt cluster. Thus, noticing to the DOS, other efficient catalysts can be discovered and the diameter distribution will be controllable by adjusting temperature, a catalyst size, and a catalyst combination without any complicated techniques and facilities.

Patterns of roof runoff contamination and their potential implications on practice and regulation of treatment and local infiltration

1996 ◽  
Vol 33 (6) ◽  
pp. 39-48 ◽  
Author(s):  
Jürgen Förster
Keyword(s):  
Heavy Metals ◽  
Metal Surfaces ◽  
Precipitation Event ◽  
Pollution Level ◽  
Runoff Water ◽  
Roof Runoff ◽  
Negative Exponential Function ◽  
Subsequent Decrease ◽  
First Flush Effect ◽  
Negative Exponential

Roof runoff water was sampled from an experimental roof system and from house roofs in the city of Bayreuth, Germany. Samples were analysed for organic micropollutants, heavy metals and sum parameters. The pollution level and the shape of the runoff profiles are dependent on the individual properties of the precipitation event and the roof, but patterns with high concentrations at the beginning of the event and a subsequent decrease (first flush effect) are very typical. For dissolved substances, the profile can often be well described by a negative exponential function. Metal surfaces on the roofs cause extreme runoff pollution with heavy metals (Cu, Zn) that constitutes an environmental hazard. It is concluded that there is a need for the development of flexible drainage strategies for surface runoff and that metal surfaces should be avoided on roofs.

scholarly journals A Computational Model for Oxygen Depletion Hypothesis in FLASH Effect

2021 ◽  
Author(s):  
Ankang Hu ◽  
Rui Qiu ◽  
Zhen Wu ◽  
Hui Zhang ◽  
Wei Bo Li ◽  
...  
Keyword(s):  
Computational Model ◽  
Dose Rate ◽  
Oxygen Concentration ◽  
Microvessel Density ◽  
Oxygen Depletion ◽  
Oxygen Distribution ◽  
Resistance Level ◽  
Negative Exponential Function ◽  
Normal Tissues ◽  
Negative Exponential

Experiments have reported low normal tissue toxicities during FLASH irradiation, but the mechanism has not been elaborated. Several hypotheses have been proposed to explain the mechanism. One hypothesis is oxygen depletion. We analyze the time-dependent change of oxygen concentration in the tissue to study the oxygen depletion hypothesis using a computational model. The effects of physical, chemical and physiological parameters on oxygen depletion were explored. The kinetic equation of the model is solved numerically using the finite difference method with rational boundary conditions. Results of oxygen distribution is supported by the experiments of oxygen-sensitivity electrodes and experiments on the expression and distribution of the hypoxia-inducible factors. The analysis of parameters shows that the steady-state oxygen distribution before irradiation is determined by the oxygen consumption rate of the tissue and the microvessel density. The change of oxygen concentration after irradiation has been found to follow a negative exponential function, and the time constant is mainly determined by the microvessel density. The change of oxygen during exposure increases with dose rate and tends to be saturated because of oxygen diffusion. When the dose rate is high enough, the same dose results in the same reduction of oxygen concentration regardless of dose rate. The analysis of the FLASH effect in the brain tissue based on this model does not support the explanation of the oxygen depletion hypothesis. The oxygen depletion hypothesis remains controversial because the oxygen in most normal tissues cannot be depleted to radiation resistance level by FLASH irradiation.

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