The scientists used a method called kriging to estimate pollution levels in groundwater by combining flow-and-transport simulations. They incorporated specific covariance models to account for the flow equations, improving the accuracy of their estimates. By using numerical covariances based on flow simulator outputs, they were able to better capture the spatial variability of contaminant concentrations. This approach was tested on synthetic and real data from an aquifer in the Chernobyl area, showing significant improvements over traditional kriging methods.