A Class-Kriging predictor for Functional Compositions with Application to Particle-Size Curves in Heterogeneous Aquifers
Friday 12th December 2014
Menafoglio, A.; Secchi, P.; Guadagnini, A.
We address the problem of characterizing the spatial field of soil particle-size curves (PSCs) within a heterogeneous aquifer system. We conceptualize the medium as a composite system, associated with an uncertain spatial arrangement of geomaterials. We tie the identification of the latter to the spatially varying arrangement of soil textural properties, which is in turn estimated by an available set of observed PSCs. We analyze these PSCs through their particle-size densities (PSDs), which are interpreted as points in the infinite-dimensional Hilbert space of functional compositions (FCs). To model the heterogeneity of the system, we introduce an original hierarchical model for FCs, conducive to a Functional Compositional Class-Kriging (FCCK) predictor. To tackle the problem of lack of information when the spatial arrangement of soil types is unobserved, we propose a novel clustering method for spatially dependent FCs. The latter allows inferring a grouping structure from sampled PSDs, consistent with our theoretical framework. This enables one to project the complete information content embedded in the set of heterogenous PSDs to unsampled locations in the system, thus providing predictions of the spatial arrangement of (a) regions associated with each identified textural class, and (b) the PSDs within each region. Our methodological developments are tested on a field application relying on a set of particle-size curves observed within an alluvial aquifer in the Neckar river valley, in Germany.