Uncertainty in Pareto fronts of land use allocation caused by spatial input data

Pursuing the single goal of maximal agricultural production in land use management has proven to involve many drawbacks, including negative environmental, economic and social impacts. Finding an optimal land use allocation involves various contradicting short-term and long-term goals depending on the location and its demands. Existing multi-objective optimization techniques can incorporate multiple goals in land use allocation, but none addresses the uncertainty introduced by the necessary spatial input data. Land use classifications, soil maps, ground water level maps or biodiversity maps are exemplary spatial data products required for land use allocation problems. These spatial data can be imprecise or inaccurate, and these errors propagate through the optimization. Hence, the results of the optimization are uncertain. The degree of this uncertainty is not quantified by current optimization methods. Here, we aim to develop and test a strategy that considers the uncertainty in spatial input data and quantifies its impact on the resulting land use allocations. In a case study of land use allocation under two objectives, maximizing agricultural production and species richness, we define the uncertainty in spatial data input and accordingly make these inputs stochastic. A Monte Carlo simulation of an evolutionary algorithm is implemented to perform the optimization. Each individual Monte Carlo sample generates one Pareto front. By combining the calculated Pareto fronts, a median Pareto front with confidence intervals is formed, which represents the uncertain Pareto front. First results indicate that the confidence interval is narrower at the two ends of the Pareto front, because at these ends spatial data input of only one of the two objectives is relevant, such that the uncertainty in the other inputs does not affect the allocation. The uncertain Pareto front can be used to estimate the robustness of a certain land allocation choice given the uncertainty caused by spatial input data.