Modeling carbon cycling on disturbed landscapes

Human activities, such as forest harvest or clearing, and many natural disturbances, such as fire and disease, affect terrestrial ecosystems on much finer spatial scales than are normally considered when analyzing biome, continental, or global patterns and responses. Such disturbances, however, impose spatial variability on ecosystem characteristics that analyses at these coarser scales must account for. An alternative to the explicit spatial treatment of the effects of disturbance is to maintain only the distributions within coarser land units of variables affected by disturbance. An area distribution function expresses the distribution of area within a land unit as a function of the density of carbon in vegetation per unit area, and a partial differential equation describes the dynamics of this distribution function in response to plant growth and land use. The area distribution equation can be forced by a variety of functions in order to simulate the responses to different disturbances. Solutions to the equation for unforced response to initial conditions and for basic forcing functions show the general characteristics of the area distribution equation and its utility in modeling landscape responses to disturbance.