Mapping efficiency and information content

This paper proposes two compound measures of mapping quality to support objective comparison of spatial prediction techniques for geostatistical mapping: (1) mapping efficiency – defined as the costs per area per amount of variation explained by the model, and (2) information production efficiency – defined as the cost per byte of effective information produced. These were inspired by concepts of complexity from mathematics and physics. Complexity i.e. the total effective information is defined as bytes remaining after compression and after rounding up the numbers using half the mapping accuracy (effective precision). It is postulated that the mapping efficiency, for an area of given size and limited budget, is basically a function of inspection intensity and mapping accuracy. Both measures are illustrated using the Meuse and Ebergötzen case studies (gstat, plotKML packages). The results demonstrate that, for mapping organic matter (Meuse data set), there is a gain in the mapping efficiency when using regression-kriging versus ordinary kriging: mapping efficiency is 7% better and the information production efficiency about 25% better (3.99 vs 3.14 EUR B−1 for the GZIP compression algorithm). For mapping sand content (Ebergötzen data set), the mapping efficiency for both ordinary kriging and regression-kriging is about the same; the information production efficiency is 29% better for regression-kriging (37.1 vs 27.7 EUR B−1 for the GZIP compression algorithm). Information production efficiency is possibly a more robust measure of mapping quality than mapping efficiency because: (1) it is scale-independent, (2) it can be more easily related to the concept of effective information content, and (3) it accounts for the extrapolation effects. The limitation of deriving the information production efficiency is that both reliable estimate of the model uncertainty and the mapping accuracy is required.