An integrated system of stand models was developed for loblolly pine in which models of different levels of resolution are related by a unified mathematical structure. A “telescoping'' system is presented in which a highly detailed overall model is specified and its components. ''collapsed" around a common set of growth and survival functions to provide structurally compatible models at each successively lower stage of resolution.
The most detailed model is a distance dependent individual tree model which simulates the growth and competitive interaction of trees in a stand. Tree basal area and height growth were modeled using a modified Chapman-Richards function in terms of potential growth, current size, relative size, crown ratio, and an index of competition. Potential growth was considered a function of site quality, age, and open-grown size relationships. Tree survival probability was described using a logistic function in terms of age, crown ratio, and competition.
The competition or point density index is a function of the size and location of neighbors. Published indices were evaluated and compared on their simple correlation with growth, multiple correlation with growth in the presence of other tree and stand measures, computer execution time, and relationships to stand level density measures. The area potentially available (APA) for each tree was chosen as the most suitable. The APA index is calculated as the area of the polygon constructed from lines which divide the distance between a tree and its neighbors. Mean APA, or average area per tree, is estimated by the inverse of trees per unit area, permitting point density to collapse to stand density, resulting in a distance independent individual tree model.
This model was collapsed dimensionally to consider trees grouped in size classes. Tree growth and survival equations are applied to the mean attributes of each size class, resulting in a size class projection model. At the lowest level of resolution, the dimensions of the model are collapsed to one "average" tree. A stand level projection model results from applying the tree growth and survival equations to the stand's average tree attributes.
At the stand level, the basal area growth function provides a transformation which, for a number of probability density functions (pdf's), will regenerate the initial pdf family. Considering a normal pdf to describe basal area distributions, a pdf-based size distribution model is presented, in which the projected parameters are expressed in terms or the growth function coefficients. Applications to other pdf families are discussed.
Preliminary tree growth and survival equation coefficients were estimated using data from a loblolly pine stand density study in North Louisiana. Structurally compatible models at each level of resolution are detailed. Considerations for numerically consistent estimates from models of different levels of resolution are discussed in terms of model specification, estimation, and implementation. Recommendations for model application and future model development are presented. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/71124 |
| Date | January 1981 |
| Creators | Daniels, Richard F. |
| Contributors | Forestry |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | vi, 105, [3] leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 7993814 |
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