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 (Ap), calculated as the area of the polygon constructed from lines which divide the distance between a tree and its neighbors. Mean Ap, 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.

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