Sensitivity of land-use pattern optimisation to variation in input data and constraints

Abstract

Spatial optimisation has been widely used in scientific studies for land-use pattern optimisation and resource allocation, often to maximise ecosystem services and/or land use performances. Such use implies its applicability in real-world spatial planning and policy development. But how suitable is spatial optimisation, especially in the context of uncertain input data and stakeholder expectations? For example, what is the impact of uncertainty associated with modelled nitrate leaching rates on land-use pattern optimisation with the objective to minimise nitrate leaching? Since spatial optimisation problems are usually constrained by stakeholder expectations or preferences, it is equally important to know how sensitive optimal land-use pattern are to changes in those expectations and preferences. In this paper, we investigate how sensitive optimal land-use patterns are to variation in input data (e.g. nitrate leaching rates) and optimisation constraints, such as stakeholder expectations in terms of agricultural production outputs. Our analysis was based on a spatial optimisation study in the Hawke's Bay area of New Zealand's North Island. The objective was to explore the landscape's limits in terms of the potential reduction in nitrate leaching. The optimisation problem was constrained by expectations for agricultural production outputs of the main agricultural land uses in this area. The spatial optimisation was based on nitrate leaching rates for each land use-land parcel combination of the case study area. Since no information was available on the uncertainties associated with the given nitrate leaching rates, we computed seven different optimisation scenarios, assuming seven different levels of uncertainties ranging from 5% to 50%. For each of those seven scenarios, we computed 500 optimisation runs and added to each run a uniformly distributed random error to the given nitrate leaching values. We then determined the allocation frequency of each land use to each land parcel for each uncertainty level. Based on the allocation frequencies, we determined the maximum allocation probability for each land parcel and uncertainty level, which represents the most likely allocated land use over 500 optimisation runs. The distributions of allocation probabilities across land parcels as well as across uncertainty levels were then used to characterise the sensitivity of the optimal land-use pattern to variation in the underlying nitrate leaching rates. To compare the landscape's potential to reduce nitrate leaching across the different uncertainty levels, we calculated the mean total nitrate leaching for the case study area for each uncertainty level (i.e. across 500 optimisation runs) and associated it with the mean maximum allocation probability for the particular uncertainty level. To analyse the impact of variation in the optimisation constraints on the optimal land-use pattern, we followed a similar approach. But instead of a random perturbation like with the nitrate leaching rates, we systematically varied the optimisation constraints by values ranging from +50% to -50% to compute a total of 14 different optimisation scenarios. However, only nine scenarios with values ranging from +10 to -50% actually represented feasible optimisation problems and yielded an optimal land-use configuration. To characterise the variation in the generated optimal land-use pattern, we also derived allocation probabilities, which referred to the nine feasible optimisation scenarios featuring different optimisation constraints. The results of the optimisation scenarios show that the potential reduction of total nitrate leaching increases with the uncertainty of the modelled nitrate leaching rates. Hence, the spatial optimisation potential increases with the variance of the input data. The mean maximum allocation probability decreased with higher uncertainty of the input data. The observed sensitivity of the land-use configuration to variation of the optimisation constraints is in general smaller than the observed sensitivity for the variation of input data. Uncertainty of input performance scores for spatial optimisation can lead to an overestimation of the actual benefit of spatial optimisation. In the Heretaunga case study area the potential spatial optimisation benefit was overestimated by more than 5% points for uncertainty levels of more than 20%. Uncertainty associated with the optimisation performance scores had overall greater impact on the uncertainty of optimal land-use allocation than the variation of optimisation constraints. Maps of maximum allocation probabilities help spatial planners identify hot spot areas for targeted land-use development and change.