Accounting for Spatial Sampling Effects in Regional Uncertainty Propagation Analysis
Gerard B.M. Heuvelink*, Dick J. Brus and Gertjan Reinds
Environmental Sciences Group, Wageningen University and Research Centre, Wageningen, the Netherlands
Abstract: Spatial uncertainty propagation analysis (UPA) aims at analysing how uncertainties in model inputs propagate through spatial models. Monte Carlo methods are often used, which estimate the output uncertainty by repeatedly running the model with inputs that are sampled from their probability distribution. Regional application of UPA usually means that the model output must be aggregated to a larger spatial support. For instance, decision makers may want to know the uncertainty about the annual nitrate leaching averaged over an entire region, whereas a model typically predicts the leaching for small plots. For models without spatial interactions there is no need to run the model at all points within the region of interest. A sufficiently large sample of locations may represent the region sufficiently well. The reduction in computational load can then be used to increase the number of Monte Carlo runs, which decreases the Monte Carlo sampling error. In this paper we analyse how a combination of analytical and numerical methods can be used to evaluate the errors introduced by Monte Carlo and spatial sampling. This is important to be able to correct for the bias inflicted by the spatial sampling, to determine how many model runs are needed to reach sufficiently accurate results and to determine the optimum ratio of the Monte Carlo and spatial sample sizes. Results are briefly illustrated with an UPA of a linear regression model that predicts the terrestrial nitrous-oxide emission for Europe.
Keywords: spatial uncertainty analysis, sampling error, Monte Carlo error, optimization, spatial aggregation