A stratified random sampling design in space and time for regional to global scale burned area product validation.

The potential research, policy and management applications of global burned area products place a high priority on rigorous, quantitative assessment of their accuracy. Such an assessment can be achieved by implementing validation methods employing design-based inference in which the independent reference data are selected via a probability sampling design. The majority of global burned area validation exercises use Landsat data to derive the independent reference data. This paper presents a three-dimensional sampling grid that allows for probability sampling of Landsat data in both space and time. To sample the globe in the spatial domain with non-overlapping sampling units, the Thiessen Scene Area (TSA) tessellation of the Landsat path/row geometry is used. The TSA grid is combined in time with the 16-day Landsat acquisition calendar to provide three-dimensional elements (voxels).This allows for implementation of stratified random sampling designs, where not only the location but also the time interval of the independent reference data is explicitly drawn by probability sampling. To illustrate this, we use a stratification methodology based on the Olson global ecoregion map and on the MODIS global active fire product. Using the global MODIS burned area product to establish a hypothetical population of reference data, we show that a sampling scheme based on the proposed stratification with equal sample allocation among strata is effective in reducing the standard errors of accuracy and area estimators compared to simple random sampling. Globally, the standard errors were reduced by 63%, 54%, 22% and 53% for overall accuracy, omission error, commission error and total burned area estimates respectively. By incorporating probability sampling in both the spatial and temporal domains, the present study establishes the foundation for rigorous design-based validation of global burned area products and, more generally, of terrestrial thematic products that have high temporal variability.