Assessing the spatial distribution of crop areas using a cross-entropy method

While crop production statistics are reported on a geopolitical - often national - basis, we often need to know, for example, the status of production or productivity within specific sub-regions, watersheds, or agro-ecological zones. Such re-aggregations are typically made using expert judgments or simple area-weighting rules. We describe a new, entropy-based approach to the plausible estimates of the spatial distribution of crop areas. Using this approach tabular crop production statistics are blended judiciously with an array of other secondary data to assess the areas of specific crops within individual 'pixels'-typically 25-100 km2 in size. The information utilized includes crop production statistics, farming system characterization, satellite-based interpretation of land cover, biophysical crop suitability assessments, and population density. An application is presented in which Brazilian state level production statistics are used to generate pixel level crop area data for eight crops. To validate the spatial allocation we aggregated the pixel estimates to obtain synthetic estimates of municipality level areas in Brazil, and compared those estimates with actual municipality statistics. The approach produced extremely promising results. We then examined the robustness of these results compared to simplified approaches to spatializing crop production statistics and showed that, while computationally intensive, the cross-entropy method does provide more reliable spatial allocations.