Standards for evaluating taper estimating systems

Kozak, A.; Smith, J. Harry G.

doi:10.5558/tfc69438-4

Cited by 72 publications

(42 citation statements)

References 6 publications

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“…The same was done for h residuals by relative diameters. These graphs, calculated by position, are very important for showing areas for which the taper functions provide especially poor or good predictions (Kozak, 2004;Kozak and Smith, 1993).…”

Section: Model Comparisonmentioning

confidence: 99%

Un modèle pour l’estimation du volume commercialisable du pin sylvestre dans les principales régions de montagne d’Espagne

2009

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Abstract• Accurate estimation of stem volume makes it possible to estimate the monetary value of one of the many commodities and services that forests provide to society, i.e. timber.• In the present study a compatible volume system for Scots pine in the major mountain ranges of Spain (the Pyrenees, Southern Iberian Range, Northern Iberian Range, Soria and Burgos Mountains, Central Range and Galician Mountains) was developed with data from 2 682 destructively sampled trees. Several well-known taper functions were evaluated. A second-order continuous-time autoregressive error structure was used to correct the inherent autocorrelation in the hierarchical data, allowing the model to be applied to irregularly spaced and unbalanced data.• The compatible segmented model of Fang et al. (2000) best described the experimental data. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the six mountain ranges analyzed.• The non-linear extra sum of squares method indicated differences in mountain range-specific taper functions. A different taper function should therefore be used for each mountain range in Spain.Mots-clés : équation de forme / modèle segmenté / équation compatible / pin sylvestre Résumé -Un modèle pour l'estimation du volume commercialisable du pin sylvestre dans les principales régions de montagne d'Espagne.• L'estimation précise du volume des tiges permet d'estimer la valeur du bois qui est un des nombreux produits et services que la forêt apporte à la société.• Dans cette étude, nous avons développé un modèle compatible de volume du pin sylvestre avec les mesures obtenues pour 2 682 arbres abattus dans les principales zones de montagne en Espagne, les Pyrénées, le sud et le nord de l'Ibérie, les montagnes de Soria et Burgos, le centre et les montagnes de Galice. Nous avons évalué plusieurs équations de profil de tiges bien connues. Pour corriger les autocorrélations inhérentes aux données hiérarchiques, nous avons utilisé un modèle d'erreur autoregressif à l'ordre 2 en temps continu, ce qui permet au modèle d'être appliqué à des données irrégulièrement espacées dans le temps et non équilibrées.• Le modèle segmenté compatible de Fang et al. (2000) décrit le mieux les données expérimentales. Il est donc recommandé pour estimer le diamètre à une hauteur donnée, la hauteur à un diamètre donné, le volume commercial et le volume total pour les six zones montagneuses étudiées.• La méthode des moindres carrés généralisés non linéaires indique des différences entre équations de profils de tiges des différentes zones montagneuses. Il faut donc utiliser une équation de profil de tige par zone de montagne en Espagne.

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Section: Model Comparisonmentioning

confidence: 99%

Un modèle pour l’estimation du volume commercialisable du pin sylvestre dans les principales régions de montagne d’Espagne

2009

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“…The same was done for volume residuals by diameter classes. These graphs, assessed by class for relative height or diameter at breast height, are very important for visualizing areas or tree size classes for which the functions provide especially good or especially poor predictions (Kozak & Smith, 1993). …”

Section: Model Comparison and Validationmentioning

confidence: 99%

Comparison of stem taper equations for eight major tree species in the Spanish Plateau

Rodríguez¹,

Lizarralde²,

Bravo

2015

For. syst.

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Aim of study: A stem taper function and a compatible merchantable volume system are compared to evaluate which provides a better description of the stem profile for the main species in central Spain.Area of study: This research was carried out in the region of Castile-Leon, located in Central Spain.Material and Methods: A total of 6,357 trees were selected for destructive sampling. All models were fitted using a first-order continuous autoregressive error structure to address the problem of autocorrelation.Main results: In terms of accuracy, the root mean square error (RMSE) in both models ranged from 0.75 to 2.72 depending on the species analyzed, presenting values similar to those reported in other studies. Small differences in the goodness-of-fit for both procedures were also found, and the Stud model provided better accuracy for 6 of the 8 species studied, with RMSE reductions of 0.5% to 8.6%. The RMSE obtained in the cross-validation phase was on average 1.22 times higher than what was obtained in the fitting phase.Research highlights: The non-linear extra sum of squares method indicated that the stem taper differs among the five softwood species and three hardwood species. In hardwoods, the first inflection point is lower than in softwoods (at around 5%) and the second inflection point is higher (at around 85%) than those of softwoods.Keywords: taper function; volume system; Central Spain; softwoods; hardwoods.

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“…4) when using the actual upper diameter measurement at 5.30 m. A lower bias does not guarantee good model performance, since large positive and negative values may algebraically counterbalance. Since it indicates the spread of the biases (residuals), the overall standard error of estimate is a better single indicator of goodness of fit (Kozak & Smith 1993). The additions of linear functions of CR and CR with CL improved model performance by reducing SEE by 1.18-3.28 % and 1.39-2.78 % for diameter and volume estimation, respectively.…”

Section: Approximation Through Taper and Volume Equations Systemmentioning

confidence: 99%

The use of tree crown variables in over-bark diameter and volume prediction models

Özçelık¹,

Diamantopoulou²,

Brooks³

2014

iForest

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© iForest -Biogeosciences and Forestry IntroductionCrown characteristics are an important component of growth and yield models. Tree crown research contributes to several key forest ecosystem attributes: biodiversity, productivity, forest management, forest environment, and wildlife (Avery & Burkhart 2002). The crown of a tree has a strong influence on stem shape, as foliage provides carbohydrates for tree growth and development of the whole tree and their vertical distribution influences stem shape (Leites & Robinson 2004, Li & Weiskittel 2010. Crown ratio (CR) is considered as an expression of the tree's photosynthetic potential, and therefore commonly included as a key variable in growth and yield models.Tree stem shape has been commonly modeled using taper models (Muhairwe 1994). Taper models are used to estimate diameter along the bole at any given height, so tree volume can then be determined based on these diameters and corresponding heights. The auxiliary variables used to increase the accuracy of existing taper equations include: (1) crown dimensions; (2) stand and site variables; and (3) upper stem diameter measurements (Trincado & Burkhart 2006). Larson (1963) reported that within the crown, stem diameters at particular heights are generally smaller when compared with trees of the same dimensions but shorter crowns. As a result, tree boles cannot be completely described as a function of bole length and diameter. In attempts to describe tree taper, numerous models of varying complexity have been advanced. In most mathematical models, taper is modeled in terms of dbh (diameter at breast height) and total height. A few researchers have considered using crown variables (e.g., crown length -CL, CR, and crown height -CH) as covariates (Newnham 1992, Leites & Robinson 2004, Jiang et al. 2007) for describing tree profiles because of the relationship between crown and stem form development, but previous studies have shown mixed results on the benefit of adding crown variables in taper models. The main crown variable utilized in taper and volume models was CR (Petersson 1999, Jiang et al. 2007, Li & Weiskittel 2010, Jiang & Liu 2011. However, CL is an interesting variable, which may influence the prediction of diameter and volume in combination with CR (Mäkela 2002). For this reason, some forms of CR and CL functions were incorporated into the tree-stem taper and volume prediction models in this study.For stem taper and volume predictions using regression analysis, an appropriate nonlinear function must first be identified, which is a very difficult task. The main reason that artificial neural network (ANN) applications have received attention is that the methodology is comparable to statistical modeling and ANNs can be seen as a complementary effort (without the restrictive assumption of a particular statistical model) or as an alternative approach to fitting nonlinear models to data. Due to the fact that Neural Networks (NNs) attempt to find the best nonlinear function based on the network's complexity, witho...

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Standards for evaluating taper estimating systems

Cited by 72 publications

References 6 publications

Un modèle pour l’estimation du volume commercialisable du pin sylvestre dans les principales régions de montagne d’Espagne

Un modèle pour l’estimation du volume commercialisable du pin sylvestre dans les principales régions de montagne d’Espagne

Comparison of stem taper equations for eight major tree species in the Spanish Plateau

The use of tree crown variables in over-bark diameter and volume prediction models

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