Dynamics in input and output coefficients for land use studies: a case study for nitrogen in crop rotations

Increasingly, model-based approaches play a role in the design and development of new land use systems. Simulation modeling may play a role in the generation of land use systems for land units, and optimization modeling (e.g. linear programming – LP) may be used in the upscaling to farm and region. In the quantification of new land use systems for land units, often equilibrium conditions with respect to soil resources are assumed, following a so-called target-oriented approach. This facilitates ex ante computation of inputs and emissions of nutrients and allows their use in static optimization models based on LP. The condition of equilibrium in soil resources is often not met, nor is it the ultimate aim. Hence, the dynamics in new systems are insufficiently dealt with. This paper presents an approach for the design of land use systems (crop rotations) and their quantification in terms of input and output coefficients, using particular yields and dynamics in soil resources as targets. Interactions between N input and output of succeeding crops are explicitly taken into account. A simple N-balance model is used describing major processes affecting soil N-dynamics. For the Koutiala region in Mali five crop rotations are evaluated that differ in target crop yield, crop choice, crop residue management and external N source. Modeled crop rotations aiming at high yields, in combination with incorporation of crop residues and legumes, result in depletion of soil N stock. Only in crop rotations aiming at high yields and with incorporation of crop residues combined with a supply of large quantities of animal manure, soil N depletion can be prevented. Four approaches are presented of how to use the dynamic input–output coefficients of these systems in land use studies using LP: (i) use of average coefficients, (ii) use of discounted coefficients, (iii) use of pessimistic estimates of coefficients in an optimization of the land use allocation followed by a recalculation of the objective values for the optimized land use with optimistic coefficients, and (iv) a combined use of systems characteristics, i.e. cumulative N-inputs of land use systems over the time horizon and the magnitude of the soil N pool at the end of the time horizon, which can be used as filters for land use systems. Though none of the approaches completely captures the dynamics in input–output coefficients, they enable a well-founded consideration of the consequences of dynamics in, for instance, soil N stocks in static optimization approaches for farm and regional studies.