The power-normal distribution: application to forest stands

Mønness, Erik Neslein

doi:10.1139/x10-246

Cited by 10 publications

(4 citation statements)

References 16 publications

(20 reference statements)

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“…It is important for the assumed models to be consistent with the distributional characteristics of the application [ 30 ]. Mønness [ 31 ] ever evaluated the power-normal distribution using the values of skewness and kurtosis. Our results noted that the shapes (reflected by skewness and kurtosis) modeled by R distribution, 3-parameter Weibull, 2-parameter Weibull and Logistic are undistorted and multiple, which is almost in accordance with the result of model accuracy.…”

Section: Discussionmentioning

confidence: 99%

Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions

Duan

Zhang

et al. 2015

PLoS ONE

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In this study, seven popular equations, including 3-parameter Weibull, 2-parameter Weibull, Gompertz, Logistic, Mitscherlich, Korf and R distribution, were used to model stand diameter distributions for exploring the relationship between the equations’ inflection point attributes and model accuracy. A database comprised of 146 diameter frequency distributions of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantations was used to demonstrate model fitting and comparison. Results showed that the inflection points of the stand diameter cumulative percentage distribution ranged from 0.4 to 0.6, showing a 1/2 close rule. The equation’s inflection point attribute was strongly related to its model accuracy. Equation with an inflection point showed much higher accuracy than that without an inflection point. The larger the effective inflection point interval of the fitting curve of the equation was, and the closer the inflection point was to 0.5 for the equations with fixed inflection points, the higher the equation’s accuracy was. It could be found that the equation’s inflection point had close relationship with skewness of diameter distribution and stand age, stand density, which provided a scientific basis for model selection of a stand diameter distribution for Chinese fir plantations and other tree species.

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Section: Discussionmentioning

confidence: 99%

Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions

Duan

Zhang

et al. 2015

PLoS ONE

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“…height, diameter, branching pattern, abiotic and biotic interference, which reflect the varied adaptive response. In silviculture and forestry practice, it is necessary to predict the variation in morphological traits [43] as the size class distribution reveals information about the stand structures (SS) and its dynamics. This type of study reveals the demographic stability and phenotypic plasticity of a species in an area.…”

Section: Introductionmentioning

confidence: 99%

Phenotypic, Geological, and Climatic Spatio-Temporal Analyses of an Exotic Grevillea robusta in the Northwestern Himalayas

et al. 2023

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The last five decades (since 1980) have witnessed the introduction of exotic trees as a popular practice in India to fulfill the demand of forest-based products for utilization in afforestation programmes. This study examines the distribution and habitat suitability of exotic Grevillea robusta trees in the northwestern Himalayas (state: Uttarakhand), focusing on the interaction between G. robusta and abiotic factors, such as climate, soil, and habitat suitability. This multipurpose agroforestry species is mainly grown by farmers as a boundary tree, windbreak, or shelterbelt and among intercrops on small farms in agroforestry systems worldwide. The results indicate that phenotypic plasticity is determined by tree height and diameter, indicating a higher frequency of young and adult trees. The study also highlights spatio-temporal modeling coupled with geological analysis to address the current distribution pattern and future habitat suitability range through MaxEnt modeling. The AUC ranged from 0.793 ± 3.6 (RCP 6.0_70) to 0.836 ± 0.008 (current) with statistical measures, such as K (0.216), NMI (0.240), and TSS (0.686), revealing the high accuracy of the model output. The variables, which include the minimum temperature of the coldest month (Bio 6), the slope (Slo), the mean temperature of the driest quarter (Bio 9), and the precipitation of the driest quarter (Bio 17), contribute significantly to the prediction of the distribution of the species in the Himalayan state. The model predicts a significant habitat suitability range for G. robusta based on bio-climatic variables, covering an area of approximately ~1641 km2 with maximal occurrence in Pauri (~321 km2) and Almora (~317 km2). Notably, the future prediction scenario corroborates with the regions of Tons (Upper Yamuna, Uttarkashi), Kalsi (Mussoorie, Dehradun), the Kedarnath Wildlife Sanctuary, and the Badrinath Forest Division for the potentially suitable areas. The climate was found to have a strong influence on the species’ distribution, as evidenced by its correlation with the Köppen–Geiger climate classification (KGCC) map. While the species demonstrated adaptability, its occurrence showed a high correlation with bedrocks containing an elevated iron content. Furthermore, the study also provides the first trees outside forests (TOF) map of G. robusta in the region, as well as insight into its future habitat suitability.

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“…The relationship between height and diameter distributions can be accounted, provided that the function relating to height and diameter can be inverted 10 . Second, theoretical height distributions were fitted directly to tree height observations and have included such shapes as the beta 11 , the Weibull 8 , the Johnson 12 , the power-normal 13 and much more. The construction and applications of bivariate distributions of diameter and height are the most used classical fields of research in forest statistics, and it continues to be an active field of research in forest mensuration and inventory, where both the diameter and height are measured on every tree.…”

Section: Introductionmentioning

confidence: 99%

A new paradigm in modelling the evolution of a stand via the distribution of tree sizes

Rupšys

Petrauskas

2017

Sci Rep

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Our study focusses on investigating a modern modelling paradigm, a bivariate stochastic process, that allows us to link individual tree variables with growth and yield stand attributes. In this paper, our aim is to introduce the mathematics of mixed effect parameters in a bivariate stochastic differential equation and to describe how such a model can be used to aid our understanding of the bivariate height and diameter distribution in a stand using a large dataset provided by the Lithuanian National Forest Inventory (LNFI). We examine tree height and diameter evolution with a Vasicek-type bivariate stochastic differential equation and mixed effect parameters. It is focused on demonstrating how new developed bivariate conditional probability density functions allowed us to calculate the evolution, in the forward and backward directions, of the mean diameter, height, dominant height, assortments, stem volume of a stand and uncertainties in these attributes for a given stand age. We estimate the parameters by considering discrete samples of the diameter and height at a given age and by using an approximated maximum likelihood procedure. The model performance criteria for the height and diameter growth models include statistical indexes and an analysis of residuals.

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The power-normal distribution: application to forest stands

Cited by 10 publications

References 16 publications

Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions

Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions

Phenotypic, Geological, and Climatic Spatio-Temporal Analyses of an Exotic Grevillea robusta in the Northwestern Himalayas

A new paradigm in modelling the evolution of a stand via the distribution of tree sizes

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