Modelling the relationship between tree diameters and heights using SBB distribution

Tewari, V. P.; Gadow, Klaus von

doi:10.1016/s0378-1127(98)00520-9

Cited by 34 publications

(14 citation statements)

References 5 publications

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“…In the Johnson's SBB distribution, the location parameter (εh) of the Johnson's SB marginal distribution of heights is usually fixed as the minimum height of the distribution, while the scale parameter (λh) of the same marginal distribution of heights is considered as the range of the distributions, i.e., as maximum height -minimum height (Schreuder & Hafley 1977, Tewari & Von Gadow 1999, Li et al 2002, Zucchini et al 2001. Some authors have considered a value of 1.3 for the location parameter when fitting the marginal distribution of heights (Siipilehto 2000, Castedo-Dorado et al 2001.…”

Section: Discussionmentioning

confidence: 99%

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Gorgoso-Varela¹,

García-Villabrille²,

Alboreca³

2016

iForest

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Methods of estimating extreme height values can be used in forest modeling to improve fits to the marginal distribution of heights in the following bivariate diameter-height models: the SBB Johnson's distribution, the bivariate beta (GDB-2) distribution, the bivariate Logit-Logistic (LL-2) distribution and the power-normal (PN) distribution. Some applications to LiDAR derived data are also possible, e.g., for error calibration. Practical applications in forest management may also be considered, e.g., for pruning. In probability theory and statistics, the generalized extreme value (GEV) distribution, also known as the Fisher-Tippett distribution, is a family of continuous probability distributions that combine the Gumbel, Fréchet and Weibull distributions. This study compared the three distributions for fitting extreme values of tree heights (maximum and minimum heights), which were measured in 185 permanent research plots in Pinus pinaster Ait.

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Section: Discussionmentioning

confidence: 99%

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Gorgoso-Varela¹,

García-Villabrille²,

Alboreca³

2016

iForest

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“…Of course they can be applied to any of the other bivariate models that are of interest in a forestry context. Bivariate distributions have been used for some time to describe the relationship between diameters and heights (Hafley and Schreuder 1976, Warren et al 1979, Tewari and Gadow 1999) and more recently also to include other tree attributes, such as height to maximum crown width or height to crown base (Uusitalo and Kivinen 1998). More exact estimation of height of maximum crown width, crown base and dead branch height can improve the estimation of branchiness and wood quality (Collin and Houllier 1992, Maguire et al 1994, Seifert 1999.…”

Section: Discussionmentioning

confidence: 99%

A model for the diameter-height distribution in an uneven-aged beech forest and a method to assess the fit of such models

Zucchini

Schmidt²,

Gadow³

2001

Silva Fenn.

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This paper illustrates the application of a mixture model to describe the bivariate diameter-height distribution of trees growing in a pure, uneven-aged beech forest. A mixture of two bivariate normal distributions is considered but the methodology is applicable to mixtures of other distributions. The model was fitted to diameter-height observations for 1242 beech trees in the protected forest Dreyberg (Solling, Germany). A considerable advantage of the model, apart from the fact that it happens to fit this large data set unusually well, is that the individual parameters all have familiar interpretations. The bivariate Johnson S BB distribution was also fitted to the data for the purpose of comparing the fits.A second issue discussed in this paper is concerned with the general question of assessing the fit of models for bivariate data. We show how a device called "pseudoresidual" enables one to investigate the fit of a bivariate model in new ways and in considerable detail. Attractive features of pseudo-residuals include the fact that they are not difficult to interpret; they can be computed using generally available statistical software and, most important of all, they enable one to examine the fit of a model by means of simple graphs.

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“…These features are reflected in a tree's further development by means of tree growth and mortality. One practical motivation is that knowledge of the between-and within-diameter-class height variations increases the possibilities for imitating different types of thinning (Hafley and Buford 1985) whereas the typical motivation is simply the ability to provide a more realistic picture of the stand structure (e.g., Tewari and Gadow 1999). Stand structure as a joint distribution of tree diameters and heights can be described by means of bivariate pdf.…”

Section: Bivariate Distribution Of Tree Diameters and Heightsmentioning

confidence: 99%

Methods and applications for improving parameter prediction models for stand structures in Finland

Siipilehto¹

2011

Diss. For.

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This thesis report attempts to improve the models for predicting forest stand structure for practical use, e.g. forest management planning (FMP) purposes in Finland. Comparisons were made between Weibull and Johnson's SB distribution and alternative regression estimation methods. Data used for preliminary studies was local but the final models were based on representative data. Models were validated mainly in terms of bias and RMSE in the main stand characteristics (e.g. volume) using independent data.The bivariate SBB distribution model was used to mimic realistic variations in tree dimensions by including within-diameter-class height variation. Using the traditional method, diameter distribution with the expected height resulted in reduced height variation, whereas the alternative bivariate method utilized the error-term of the height model. The lack of models for FMP was covered to some extent by the models for peatland and juvenile stands. The validation of these models showed that the more sophisticated regression estimation methods provided slightly improved accuracy.A flexible prediction and application for stand structure consisted of seemingly unrelated regression models for eight stand characteristics, the parameters of three optional distributions and Näslund's height curve. The cross-model covariance structure was used for linear prediction application, in which the expected values of the models were calibrated with the known stand characteristics. This provided a framework to validate the optional distributions and the optional set of stand characteristics. Height distribution is recommended for the earliest state of stands because of its continuous feature. From the mean height of about 4 m, Weibull dbh-frequency distribution is recommended in young stands if the input variables consist of arithmetic stand characteristics. In advanced stands, basal area-dbh distribution models are recommended. Näslund's height curve proved useful. Some efficient transformations of stand characteristics are introduced, e.g. the shape index, which combined the basal area, the stem number and the median diameter. Shape index enabled SB model for peatland stands to detect large variation in stand densities. This model also demonstrated reasonable behaviour for stands in mineral soils.Keywords: stand structure, size distribution, linear prediction, height-diameter relationship, stand characteristics, regression estimation 4 ACKNOWLEDGEMENTSThe basic work was done under a project called "Stand structure, competition dynamics and site productivity in growth models" and later in the project "Prediction and simulation of stand dynamics", led by Dr. Risto Ojansuu. Most of the models included in my thesis have been implemented in a MOTTI simulator in the project "Decision support system for stand management" led by Dr. Jari Hynynen. The work was carried out by the Finnish Forest Research Institute (Metla) in Vantaa.I wish to express my warmest thanks to my supervisors, Prof. Annika Kangas and Dr. Lauri Mehtätalo. Laur...

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Modelling the relationship between tree diameters and heights using SBB distribution

Cited by 34 publications

References 5 publications

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

A model for the diameter-height distribution in an uneven-aged beech forest and a method to assess the fit of such models

Methods and applications for improving parameter prediction models for stand structures in Finland

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