Integer Programming (IP) formulation for minimizing sediment delivery in a watershed by reforestation of optimal sites

Several approaches exist to model the production, transport and delivery of water and sediment flows in watersheds but none of these are dealing with spatial optimality requirements. However, policy and decision makers dealing with environmental conservation and land use planning often require identifying potential sites for contributing to minimize sediment flow reaching riverbeds. This is the case of reforestation initiatives, which can have sediment flow minimization among their objectives. This paper proposes an Integer Programming (IP) formulation for selecting a predefined number of locations to minimize sediment load at a watershed outlet. Although the core structure of the IP model can be applied for different sorts of flow, the formulation is targeted to minimization of sediment delivery. Several experiments are performed for two watersheds in South Dakota in the USA. The results are in agreement with expert assessments of erosion levels, slopes and distances to the riverbeds, which in turn allows concluding that this approach is suitable for minimizing sediment flow.