Combining two soil property rasters using an adaptive gating approach

Given the wide variety of ways one can measure and record soil properties, it is not uncommon to have multiple overlapping predictivemaps for a particular soil property. One is then faced with the challenge of choosing the best prediction at a particular point, either by selecting one of the maps, or by combining them together in some optimal manner. This question was recently examined in detail when Malone et al. (2014) compared four different methods for combining a digital soil mapping product with a disaggregation product based on legacy data. These authors also examined the issue of how to compute confidence intervals for the resulting map based on confidence intervals associated with the original input products. In this paper, we propose a new method to combine models called adaptive gating, which is inspired by the use of gating functions in mixture of experts, a machine learning approach to forming hierarchical classifiers. We compare it here with two standard approaches - inverse-variance weights and a regression based approach. One of the benefits of the adaptive gating approach is that it allows weights to vary based on covariate information or across geographic space. As such, this presents a method that explicitly takes full advantage of the spatial nature of the maps we are trying to blend. We also suggest a conservative method for combining confidence intervals. We show that the root mean-squared error of predictions from the adaptive gating approach is similar to that of other standard approaches under cross-validation. However under independent validation the adaptive gating approach works better than the alternatives and as such it warrants further study in other areas of application and further development to reduce its computational complexity.