Título:	A mathematical expression of stem form and volume for loblolly pine in Southern Brazil.
Autor:	AHRENS, S.
Afiliación:	SERGIO AHRENS, CNPF.
Año:	1980
Referencia:	1980.
Páginas:	59 f.
Descripción:	The purpose of this study was essentially the investigation of stem form of planted loblolly pine and its analytical expression with a mathematical function. By definition, integration of such a developed taper model provides a volume function. Data where obtained in a loblolly pine plantation located in southern Brazil. A modified Hohenald's thodof tree stem measurement was used to collect the data needed for the analysis. Diameter inside bark were measured at seven relative positions along each of 188 stems. Previous stem studies were mostly bad on simple models or on the use of polynomials. Several of those investigators tried to define a universal taper model, but conflicting results were reported. On the other land, those few studies on witch principal component analysis was used, have demonstrated consistency in their conclusions. This refers to the algorithm, not to the structure of the final equation itself. In this research study, a first attempt was made using a third-degree polynomial. However, results were biased and discouraging. Alternatives to improve that taper equation were initially considered, such as the inclusion of an additional independent variable to express the inflection point, or grouping the data by size. Nevertheless, that procedure was abandoned and a multidimensional and more flexible approach was finally used. The objective of this study was successfully achieved with the use of principal component analysis, a multivariate exploratory technique. The procedure consisted of squares and cross-products matrix obtained from the data matrix of seven [positional radii(diameters)and 188 stems. The solution for the eigen-equation provided seven eigenvalues or latent roots, and seven associated column eigevenctors. Performing that matrix solution algebraically equivalent to transforming a set of correlated variables into a new set of uncorrelated variables. L=stem local length(meters) above a 15.0 cm stump height. Total volume inside bark was predicted for all 188 sample stems by using both procedures:the volume function obtained by integration of the taper model and with Hohenadl's method. Percent residual of the volume estimates obtained with the taper derived function over those determined with Hohenadl's procedure, ranged from -30.60 to 28.50. The magnitude of the residuals as well as their consistent distribution over most of the data size range,were considered adequate for the purpose of this study. After having evaluated the results obtained it was concluded that principal component analysis has proven to be an efficient means for the objective has been met satisfactory. Actuary of the prediction ability of the taper-volume systems developed can be significantly improved by measurement of diameters at a larger number of relative positions,perhaps 10 or 20. Actually only volume inside bark was computed. However the main justification for the development of taper volume systems is its flexibility in regard to the volume inside limits may be accordingly determined. Among the previous stem form studies observed in the literature,some investigators tried to developed a "universal taper function". However, such a model must take in account all possible sources of stem form variability: among others species, age, site, stand, density and past management practices such as pruning and thinning. It is evident that this is an extremely difficult task. Rather than seeking a "cooking"formula this author believes that much better and efficient results will be obtained by grouping the data as much an is possible and convenient. This context, principal component analysis is a technique of great potential when the reduction of data dimensionally is desirable. A universal taper function will not be produced by principal component analysis. In the taper model building process, the number and nature of the independent variables may vary with each new data set. However, if properly applied and interpreted, this multivariate exploratory techinique may be considered as an adequate algorithm the investigation of stem form under most of the circumstances.
Thesagro:	Modelo Matemático Pinus Taeda Volume
NAL Thesaurus:	mathematical models
Notas:	Thesis (Master of Science) - Faculty of the Graduate College, Oklahoma State University, Oklahoma.
Tipo de Material:	Teses
Acceso:	openAccess
Aparece en las colecciones:	Tese/dissertação (CNPF)