Simple, flexible, trigonometric taper equations

Thomas, Charles E.; Parresol, Bernard R.

doi:10.1139/x91-157

Cited by 59 publications

(47 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A large number of compatible taper-volume systems based on type (1) have been created for oak species in Greece, America, Denmark, Spain and Mexico (Hilt 1980, Thomas & Parresol 1991, Tarp-Johansen et al 1997, Pompa-García et al 2009, Kitikidou 2010. Simple equations (Hilt 1980, Thomas & Parresol 1991, Kitikidou 2010, variable exponent equations (Tarp-Johansen et al 1997) or segmented-polynomial equations (Pompa-García et al 2009) were chosen for taper modelling.…”

Section: Introductionmentioning

confidence: 99%

“…Simple equations (Hilt 1980, Thomas & Parresol 1991, Kitikidou 2010, variable exponent equations (Tarp-Johansen et al 1997) or segmented-polynomial equations (Pompa-García et al 2009) were chosen for taper modelling. There has been no similar research for Quercus variabilis Blume, an important broadleaf tree species in North China, prior to the study reported here.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Compatible taper-volume models of Quercus variabilis Blume forests in north China

Zheng¹,

Wang²,

Jia³

et al. 2017

iForest

View full text Add to dashboard Cite

Compatible taper and volume models were created for Quercus variabilis Blume (cork oak) forests in North China. 174 trees were felled to obtain stem analysis data. Linear mixed effects analyses were used in modelling. Firstly, a bark thickness model was built. Then diameter at breast height over bark (DBHob) for the inner layers of the 174 trees could be calculated, based on which a total volume model was built. The estimated volume and a specific parameter restriction were then substituted into a polynomial taper model, finally the taper model was fitted and compatible taper and volume models were obtained. Four sets of models based on different data sets were separately built and compared through coefficients of determination (R 2 ), root mean square error (RMSE), value of Akaike's information criterion (AIC), residuals plots and histograms of residuals. Models based on data of the analyzed stems without ramicorns and simultaneously with relative diameter under 1.5 were chosen as the most precise. Further testing of the chosen models using the jackknife method for the bark thickness and total volume models and a validation data set for the taper model verified that those models can be used to predict bark thickness, diameter at a specific point along the stem, merchantable volume and total stem volume of cork oak forests in North China within specific tree diameter at breast height and height ranges.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compatible taper-volume models of Quercus variabilis Blume forests in north China

Zheng¹,

Wang²,

Jia³

et al. 2017

iForest

View full text Add to dashboard Cite

show abstract

“…La literatura actual incluye modelos de ahusamiento lineales (Allen, 1991;Bruce et al, 1968;Kozak, Munro, & Smith, 1969;Lowell, 1986;Real & Moore, 1986;Renteria & Ramirez, 1998), no lineales (Demaerschalk, 1972(Demaerschalk, , 1973Sharma & Oderwald, 2001;Sharma & Zhang, 2004), segmentados (Cao, Burkhart, & Max, 1980;Max & Burkhart, 1976;Parresol, Hotvedt, & Cao, 1987;Valenti & Cao, 1986) y trigonométricos (Thomas & Parresol, 1991). Esa gama incluye desde modelos diferenciables e integrables, hasta modelos que requieren de la integración numérica para la obtención del volumen del fuste.…”

Section: Introductionunclassified

Modelo de ahusamiento por tipo de suelo para Pinus radiata en las regiones del Biobío y la Araucanía, Chile

Rodríguez-Toro¹,

Rubilar²,

Muñoz-Sáez³

et al. 2016

Rev Cha Se Cie For y del Amb

View full text Add to dashboard Cite

Se presenta un nuevo modelo de ahusamiento generalizado en Pinus radiata en algunos tipos de suelo. Este es un modelo no lineal ajustado con datos de 264 árboles con edades entre 15 y 31 años, cosechados en 27 rodales localizados en 11 comunas de las regiones del Biobío y la Araucanía, Chile, en tres diferentes tipos de suelos (arenas volcánicas, cenizas volcánicas y sedimentos de origen marino). La generalización del modelo se logró incorporando variables de estado del rodal, y la posterior simplificación del mismo, incorporando la variabilidad del sitio de manera implícita en sus parámetros. La función de volumen obtenida de la integración numérica del modelo de ahusamiento predice más de 97 % de la variación del volumen del fuste sin corteza estimado mediante la fórmula de Smalian, en los tres tipos de suelo.

show abstract

“…Kozak et al, 1969), logarithmic (Demaerschalk, 1972), trigonometric (Thomas & Parresol, 1991), and other forms (e.g. Biging, 1984) have been developed for trees from a wide range of species and geographical areas.…”

Section: Introductionmentioning

confidence: 99%

Input point distribution for regular stem form spline modeling

Kuželka¹,

Marušák²

2015

For. syst.

View full text Add to dashboard Cite

RESEARCH ARTICLE OPEN ACCESSand are considered as the most accurate models (Rojo et al., 2005). Both scientific and practical applications in recent forestry often require reconstruction of stem curve of an individual stem, especially within the context of exploitation of recently evolving techniques of data acquisition, as terrestrial laser scanners (Lovell et al., 2011), terrestrial close-range photogrammetry (Hapca et al., 2007), and other close-range remote sensing techniques. Splines are a useful tool allowing for interpolation or approximation of a series of discrete points representing stem diameters at given heights in order to obtain the model the stem curve.The term spline is a general expression for a wide class of functions defined piecewise usually by polynomial functions. The most commonly used spline is the cubic interpolation spline. It is frequently used to describe stem form (Lahtinen & Laasasenaho, 1979) Input point distribution for regular stem form spline modeling Karel Kuželka* and Róbert Marušák Fakulta lesnická a dřevařská, Česká zemědělská univerzita v Praze, Kamýcká 1176, Praha 6 -Suchdol, 165 21 Abstract Aim of study: To optimize an interpolation method and distribution of measured diameters to represent regular stem form of coniferous trees using a set of discrete points.Area of study: Central-Bohemian highlands, Czech Republic; a region that represents average stand conditions of production forests of Norway spruce (Picea abies [L.] Karst.) in central Europe.Material and methods: The accuracy of stem curves modeled using natural cubic splines from a set of measured diameters was evaluated for 85 closely measured stems of Norway spruce using five statistical indicators and compared to the accuracy of three additional models based on different spline types selected for their ability to represent stem curves. The optimal positions to measure diameters were identified using an aggregate objective function approach.Main results: The optimal positions of the input points vary depending on the properties of each spline type. If the optimal input points for each spline are used, then all spline types are able to give reasonable results with higher numbers of input points. The commonly used natural cubic spline was outperformed by other spline types. The lowest errors occur by interpolating the points using the Catmull-Rom spline, which gives accurate and unbiased volume estimates, even with only five input points.Research highlights: The study contributes to more accurate representation of stem form and therefore more accurate estimation of stem volume using data obtained from terrestrial imagery or other close-range remote sensing methods.

show abstract

Simple, flexible, trigonometric taper equations

Cited by 59 publications

References 4 publications

Compatible taper-volume models of Quercus variabilis Blume forests in north China

Compatible taper-volume models of Quercus variabilis Blume forests in north China

Modelo de ahusamiento por tipo de suelo para Pinus radiata en las regiones del Biobío y la Araucanía, Chile

Input point distribution for regular stem form spline modeling

Contact Info

Product

Resources

About