An integrated system of forest stand models

Abstract

An integrated system of stand models has been developed in which models of different levels of resolution are related in a unified mathematical structure. Detailed models are specified, and from them a set of growth and survival functions is derived to produce models structurally compatible at lower stages of resolution. The most detailed model is a distance-dependent individual-tree model that simulates the growth and competitive interaction of trees in a stand. Tree basal area and height growth were modelled 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 expressed as a function of site quality, age, and open-grown size. Tree survival probability was described using a logistic function in terms of age, crown ratio, and competition. The point density measure used was area potentially available ( A p), calculated as the area of the polygon constructed from lines which divide the distance between a tree and its neighbors. Mean A p, or average area per tree, is estimated as the inverse of the number of trees per unit area, so that point density reduces to stand density and a distance-independent individual-tree model results. The distance-independent individual tree model was collapsed to consider trees grouped in size classes. Tree growth and survival equations were applied to the mean attributes of each size class, resulting in a size-class projection model. Following through, the dimensions of the model were collapsed to an ‘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 was developed, in which the projected parameters were expressed in terms of the growth function coefficients.