Analytical model of carbon storage in the trees, soils, and wood products of managed forests.

The carbon balance between managed forests and the atmosphere depends critically on the frequency and intensity of harvesting, and the lifetime of harvested products. To assess more quantitatively the nature of this dependence, a theoretical analysis, previously applied to carbon storage in trees and wood products only, is extended here to include the carbon in forest floor detritus and soil. A dimensionless combination of the parameters of the model, alpha, with critical value alpha(c), is identified such that for alpha < alpha(c), the conversion of old-growth forest to managed forest releases carbon to the atmosphere in the long term. Parameter alpha is given by the combination f(t)D/T(*), where f(t) is the fraction of old-growth forest carbon stored in trees, D is the residence time of harvested biomass (wood products and slash debris) within the system, and T(*) is the rotation period for maximum sustained yield (maximum mean annual increment). The critical value alpha(c), typically in the range 0.5-0.7, is derived for a variety of forest types. Parameter alpha determines the degree to which the carbon accumulated in harvested biomass offsets the loss of carbon in trees due to felling and in soils due to reduced litter input. When alpha > alpha(c), long-term carbon storage is optimized by harvesting for maximum sustained yield.