Land use decision modeling with dynamically updated soil carbon emission rates

Soil carbon can be sequestered through different land management options depending on the soil carbon status at the beginning of a management period. This initial status results from a given soil management history in a given soil climate regime. Similarly, the prediction of future carbon storage depends on the time sequence of future soil management. Unfortunately, the number of possible management trajectories reaches non-computable levels so fast that explicit representations of management trajectories are impractical for most existing land use decision models. Consequently, the impact of different management trajectories has been ignored. This article proposes a computationally feasible mathematical programming method for integration of soil status dependent sequestration rates in land use decision optimization models. The soil status is represented by an array of adjacent status classes. For each combination of soil management and initial soil status class, transition probabilities of moving into a new or staying in the same status class are computed. Subsequently, these probabilities are used in dynamic equations to update the soil status level before and after each new soil management period. To illustrate the impacts of the proposed method, a simple hypothetical land use decision model is solved for alternative specifications.