Means and covariance functions for geostatistical compositional data: an axiomatic approach

This work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented. As a first result, it is shown that the weighted arithmetic mean is the only central tendency characteristic satisfying a small set of axioms, namely continuity, reflexivity and marginal stability. Moreover, this set of axioms also implies that the weights must be identical for all parts of the composition. This result has deep consequences on the spatial multivariate covariance modeling of compositional data. In a geostatistical setting, it is shown as a second result that the proportional model of covariance functions (i.e., the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging weights for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability

Subannual models for catchment management: Evaluating model performance on three European catchments

Models' abilities to predict nutrient losses at subannual timesteps is highly significant for evaluating policy measures, as it enables trends and the frequency of exceedance of water quality thresholds to be predicted. Subannual predictions also permit assessments of seasonality in nutrient concentrations, which are necessary to determine susceptibility to eutrophic conditions and the impact of management practices on water quality. Predictions of subannual concentrations are pertinent to EC Directives, whereas load estimates are relevant to the 50% target reduction in nutrient loading to the maritime area under OSPAR. This article considers the ability of four models (ranging from conceptual to fully mechanistic), to predict river flows, concentrations and loads of nitrogen and phosphorus on a subannual basis in catchments in Norway, England, and Italy. Results demonstrate that model performance deemed satisfactory on an annual basis may conceal considerable divergence in performance when scrutinised on a weekly or monthly basis. In most cases the four models performed satisfactorily, and mismatches between measurements and model predictions were primarily ascribed to the limitations in input data (soils in the Norwegian catchment; weather in the Italian catchment). However, results identified limitations in model conceptualisation associated with the damping and lagging effect of a large lake leading to contrasts in model performance upstream and downstream of this feature in the Norwegian catchment. For SWAT applied to the Norwegian catchment, although flow predictions were reasonable, the large number of parameters requiring identification, and the lack of familiarity with this environment, led to poor predictions of river nutrient concentrations

A novel downscaling procedure for compositional data in the Aitchison geometry with application to soil texture data

In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity, accounting for the scale invariance and relative scale of these data. We show that the method can be used in a block sequential Gaussian simulation framework in order to assess the variability of downscaled quantities. Finally, to validate the method, we test it first in an idealized scenario and then apply it for the downscaling of digital soil maps on a more realistic case study. The digital soil maps for the realistic case study are obtained from SoilGrids, a system for automated soil mapping based on state-of-the-art spatial predictions methods