A novel downscaling procedure for compositional data in the Aitchison geometry with application to soil texture data
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ORIGINAL PAPER
A novel downscaling procedure for compositional data in the Aitchison geometry with application to soil texture data Federico Gatti1 • Alessandra Menafoglio1 Monica Papini2 • Laura Longoni2
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Niccolo` Togni1 • Luca Bonaventura1 • Davide Brambilla2
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Accepted: 7 October 2020 The Author(s) 2020
Abstract 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. Keywords Geostatistics Block sequential Gaussian simulation Area-to-point kriging Isometric log-ratios
1 Introduction Uncertainty Quantification (UQ) is a crucial aspect for numerical tools intended to simulate physical processes, since it is important to provide an extensive analysis of the uncertainty of the outputs related to the variability of the inputs. Classical methods to perform this task are based on Monte Carlo (MC) simulations (Kalos and Whitlock 2009). Here, an ensemble of realizations of the input parameters is used to feed a mathematical/numerical model, aiming to assess the distribution of the response in the face of uncertain inputs. In this broad framework, whenever parameters are characterized by a spatial distribution, geostatistical stochastic simulation can be employed to generate input scenarios for the model (Brown et al. 2002). The geostatistical approach allows one to account for the spatial dependence characterizing the input parameters and to model the spatial structure expected for the realizations & Alessandra Menafoglio [email protected] 1
MOX-Department of Mathematics, Politecnico di Milano, Milan, Italy
2
Department of Civil and Environmental Engineering, Politecnico di Milano, Milan, Italy
(range of variability, degree of smoothness) through a spatial covariance function. Nonetheless, sound geostatistical simulation needs to take into account the possible constraints of the data, particularly when these represent compositional information. For instance, soil moisture retention plays an important role in models that simulate hydrogeological processes and depends on a number of terrain properties, such as the soil texture. The latter in turn is determined by particle-size fractions (psfs), i.e. the relative percentages, in terms of soil composition, of clay, silt and sand, the three categories in which grains of fine earth are divided depending on their size, see e.g. Martı´n et al.
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