Combining point and regular lattice data in geostatistical interpolation

This work studies how to include both point and areal measurements when estimating gaussian fields by kriging. To achieve this objective, three geostatistical approaches are considered for the areal distributed data: (a) regionalized measurements that are geographically referenced by their centroid as if they were point measurements, (b) regionalized measurements that are explicitly accounted by formally computing all the needed covariances (i.e. area-to-area, area-to-point and point-to-point covariances, respectively) and (c) regionalized measurements that are used as an external drift variable. Results indicate that the measurement error corresponding to the areal data plays a key role to decide when the spatial support of the areal measurements is relevant. For small measurement errors, it is necessary to explicitly consider the spatial support of the areal measurements to avoid large estimation variances. For large measurement errors, the difference between defining areal measurements by using their actual spatial support and defining areal measurements by referencing them by their centroids (i.e. gravity centre) is small. In this situation, it is possible to use the areal measurements as an external drift instead of merging both types of information (i.e. point and areal data) as measurements for kriging. In this case, the cross-validation analysis shows a larger coefficient of determination, similar average kriging variance and smaller mean square error than the obtained in the case of merging point and areal measurements for kriging.