A Carbon-balance Model of Stand Growth: a Derivation Employing Pipe-model Theory and the Self-thinning Rule

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Abstract
A carbon-balance model of the growth of an even-aged, self-thinning, mono-specific stand of trees is derived using a structural framework based on pipe-model theory. Within the pipe-model framework, dry matter arising from extension of roots and shoots is separable from that arising from the cross-sectional expansion of stems. This permits the derivation of models describing the growth of average stem length, total basal area, and total volume of the stand. Variations of these models are described for two situations: (1) where the annual rates of substrate production and feeder-root turnover can be assumed constant over time; and (2) where these rates are expected to change over time, such as in polluted environments. The model describing the growth of stand volume for the first situation fits published yield tables. Growth-rate models applicable to individual trees are also described.

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