Kriging prediction for functional compositional data and application to particle-size curves

We present a new geometric approach to krige functional compositional data which embraces the viewpoints of both Functional and Compositional Data Analysis. Our theoretical framework enables one to characterize and predict random fields valued in the Hilbert space of functional compositions endowed with the Aitchison geometry. We show the application of the methodology to a field case scenario dealing with particle-size data collected within a heterogeneous aquifer near Tubingen, Germany. We consider particle-size densities, interpreted as functional compositional data, and perform kriging of these curves to obtain a complete characterization of the soil textural properties within the aquifer