Uncertainty of spatial averages and totals of natural resource maps

Global, continental and regional maps of concentrations, stocks and fluxes of natural resources provide baseline data to assess how ecosystems respond to human disturbance and global warming. They are also used as input to numerous modelling efforts. But these maps suffer from multiple error sources and hence it is good practice to report estimates of the associated map uncertainty, so that users can evaluate their fitness for use. In this presentation we address the question of how to obtain the uncertainty of spatial aggregates of the map predictions. This is needed when the mapped variable is reported as an average or total for subareas within the study area, such as for rectangular grid cells, administrative units or bioclimatic domains, or for the study area as a whole. We first explain why quantification of uncertainty of spatial aggregates is more complex than uncertainty quantification at point support, because it must account for spatial autocorrelation of the map errors. We describe how this can be done with block kriging and illustrate this method in a case study of mapping the topsoil organic carbon content at various administrative aggregation levels in mainland France. Next, we propose an approach that avoids the numerical complexity of block kriging and is feasible for large-scale studies where maps are typically made using machine learning. Our approach relies on Monte Carlo integration to derive the uncertainty of the spatial average or total from point support prediction errors. We account for spatial autocorrelation of the map error by geostatistical modelling of the standardized map error. The methodology is illustrated with mapping aboveground biomass and deriving the associated uncertainty for various block supports in a region in Western Africa. Both case studies clearly show the need to account for spatial autocorrelation in order to get realistic estimates of the uncertainty of spatial averages and totals.