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In this work we describe a first version of the simulation tool developed within the SMART-SED project. The two main components of the SMART-SED model consist in a data preprocessing tool and in a robust numerical solver, which does not require a priori identification of river beds and other surface run-off areas, thus being especially useful to provide accurate input data to more localized landslide and debris-flow models. Furthermore, a geostatistical tool is available to downscale SoilGrids particle size fractions (psf) data to a given resolution. The psf data is employed also within the SCS-CN method, used to model the infiltration process. The results of a complete numerical simulation are reported and possible future developments of the model are discussed.

Georeferenced compositional data are prominent in many scientific fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose, a novel class of transformations, named the Isometric $\alpha$-transformation ($\alpha$-IT), is proposed, which encompasses the traditional Isometric Log-Ratio (ILR) transformation. It is shown that the ILR is the limit case of the $\alpha$-IT as $\alpha$ tends to 0 and that $\alpha=1$ corresponds to a linear transformation of the data. Unlike the ILR, the proposed transformation accepts 0s in the compositions when $\alpha>0$. Maximum likelihood estimation of the parameter $\alpha$ is established. Prediction using kriging on $\alpha$-IT transformed data is validated on synthetic spatial compositional data, using prediction scores computed either in the geometry induced by the $\alpha$-IT, or in the simplex. Application to land cover data shows that the relative superiority of the various approaches w.r.t. a prediction objective depends on whether the compositions contained any zero component. When all components are positive, the limit cases (ILR or linear transformations) are optimal for none of the considered metrics. An intermediate geometry, corresponding to the $\alpha$-IT with maximum likelihood estimate, better describes the dataset in a geostatistical setting. When the amount of compositions with 0s is not negligible, some side-effects of the transformation gets amplified as $\alpha$ decreases, entailing poor kriging performances both within the $\alpha$-IT geometry and for metrics in the simplex., Comment: 31 pages and 13 Figures. Supplementary material with 3 Figures

We propose and exemplify a framework to assess Natural Background Levels (NBLs) of target chemical species in large-scale groundwater bodies based on the context of Object Oriented Spatial Statistics. The approach enables one to fully exploit the richness of the information content embedded in the probability density function (PDF) of the variables of interest, as estimated from historical records of chemical observations. As such, the population of the entire distribution functions of NBL concentrations monitored across a network of monitoring boreholes across a given aquifer is considered as the object of the spatial analysis. Our approach starkly differs from previous studies which are mainly focused on the estimation of NBLs on the basis of the median or selected quantiles of chemical concentrations, thus resulting in information loss and limitations related to the need to invoke parametric assumptions to obtain further summary statistics in addition to those considered for the spatial analysis. Our work enables one to (i) assess spatial dependencies among observed PDFs of natural background concentrations, (ii) provide spatially distributed kriging predictions of NBLs, as well as (iii) yield a robust quantification of the ensuing uncertainty and probability of exceeding given threshold concentration values via stochastic simulation. We illustrate the approach by considering the (probabilistic) characterization of spatially variable NBLs of ammonium and arsenic detected at a monitoring network across a large scale confined groundwater body in Northern Italy.

SMART-SED is a project aimed at developing an innovative framework for the numerical simulation of sediment motion in river catchments, intended to be used by local territorial management institutions and professionals to design proper strategies for the mitigation of hydrogeological instability. Uncertainty analysis is an intrinsic feature of models simulating natural processes. In order to perform an effective uncertainty quantification, it is necessary to properly identify the variability of the input parameters and to design stochastic simulation methods able to provide realistic realisations, based on the available data. This thesis focuses on the use of digital soil maps for the prediction and stochastic simulation of terrain-related quantities used for the estimation of the input parameters of the SMART-SED model. The digital maps are obtained from SoilGrids, a system for automated soil mapping based on state-of-the-art spatial predictions methods. Innovative approaches are introduced to account for the limitations of SoilGrids data (low resolution, inaccuracy) and for the specificities of the variables in exam. Although the focus is on the SMART- SED project, the methods proposed can be generally used for geostatistical modelling at a local scale using auxiliary coarse information obtained through remote sensing or from previously fitted digital maps.

We propose a new methodology for the analysis of spatial fields of object data distributed over complex domains. Our approach enables to jointly handle both data and domain complexities, through a divide et impera approach. As a key element of innovation, we propose to use a random domain decomposition, whose realizations define sets of homogeneous sub-regions where to perform simple, independent, weak local analyses (divide), eventually aggregated into a final strong one (impera). In this broad framework, the complexity of the domain (e.g., strong concavities, holes or barriers) can be accounted for by defining its partitions on the basis of a suitable metric, which allows to properly represent the adjacency relationships among the complex data (such as scalar, functional or constrained data) over the domain. As an illustration of the potential of the methodology, we consider the analysis and spatial prediction (Kriging) of the probability density function of dissolved oxygen in the Chesapeake Bay.

The problem of performing functional linear regression when the response variable is represented as a probability density function (PDF) is addressed. PDFs are interpreted as functional compositions, which are objects carrying primarily relative information. In this context, the unit integral constraint allows to single out one of the possible representations of a class of equivalent measures. On these bases, a function-on-scalar regression model with distributional response is proposed, by relying on the theory of Bayes Hilbert spaces. The geometry of Bayes spaces allows capturing all the key inherent features of distributional data (e.g., scale invariance, relative scale). A B-spline basis expansion combined with a functional version of the centered log-ratio transformation is utilized for actual computations. For this purpose, a new key result is proved to characterize B-spline representations in Bayes spaces. The potential of the methodological developments is shown on simulated data and a real case study, dealing with metabolomics data. A bootstrap-based study is performed for the uncertainty quantification of the obtained estimates.

In this paper we propose Universal trace co-kriging, a novel methodology for interpolation of multivariate Hilbert space valued functional data. Such data commonly arises in multi-fidelity numerical modeling of the subsurface and it is a part of many modern uncertainty quantification studies. Besides theoretical developments we also present methodological evaluation and comparisons with the recently published projection based approach by Bohorquez et al. (Stoch Environ Res Risk Assess 31(1):53–70, 2016. https://doi.org/10.1007/s00477-016-1266-y ). Our evaluations and analyses were performed on synthetic (oil reservoir) and real field (uranium contamination) subsurface uncertainty quantification case studies. Monte Carlo analyses were conducted to draw important conclusions and to provide practical guidelines for all future practitioners.

We address the problem of characterizing spatially variable Natural Background Levels (NBLs) of concentrations of chemical species of environmental concern in a large-scale groundwater body. Assessment of NBLs is critical to identify significant trends of (possibly hazardous) chemical concentrations in aquifer systems, the latter being typically associated with spatially heterogeneous hydrogeochemical characteristics. Our study considers the entire probability density function (PDF) of the concentration of the chemical species of interest as atom of the statistical analysis. These PDFs are estimated across a network of observation boreholes in the investigated spatial domain, and modeled as random points in a Bayes Hilbert space, in the context of Object Oriented Data Analysis. This approach enables one to take advantage of the entire information content provided by these objects for the purpose of spatial prediction and uncertainty quantification. As a key element of innovation, we investigate the use of depth measures for distributional data with the distinctive aims of ( i ) detecting central and outlying NBL distributions in the dataset, and ( i i ) building prediction regions for NBL distribution at unsampled locations. We illustrate the results of the proposed approach to the analysis of NBLs of a selected chemical species detected at an environmental monitoring network within a large-scale alluvial aquifer in Northern Italy.

This paper proposes a novel nonparametric approach to model and reveal differences in the geochemical properties of the soil, when these are described by space–time measurements collected in a spatial region naturally divided into two parts. The investigation is motivated by a real study on a space–time geochemical data set, consisting of measurements of potassium chloride pH, water pH, and percentage of organic carbon collected during the growing season in the agricultural and forest areas of a site near Brno (Czech Republic). These data are here modeled as spatially distributed functions of time. A permutation approach is introduced to test for the effect of covariates in a spatial functional regression model with heteroscedastic residuals. In this context, the proposed method accounts for the heterogeneous spatial structure of the data by grounding on a permutation scheme for estimated residuals of the functional model. Here, a weighted least squares model is fitted to the observations, leading to asymptotically exchangeable and, thus, permutable residuals. An extensive simulation study shows that the proposed testing procedure outperforms the competitor approaches that neglect the spatial structure, both in terms of power and size. The results of modeling and testing on the case study are shown and discussed.

Working with geometallurgical variables presents different challenges in mathematical geosciences, particularly, scale problems (van den Boogaart and Tolosana-Delgado, 2018). Geometallurgical data with distributional scale requires theoretical and practical developments. Methods for statistical interpolation and simulation of distributional data in space have been recently proposed by (Menafoglio et al., 2014, 2016). However, no method is available to sequentially incorporate new information into spatial models. One of the most promising implementations of such sequential information update in resource modelling estimation industry are data assimilation techniques (Wambeke and Benndorf, 2017; Benndorf, 2015). These techniques are becoming popular due to the ability of dealing with large amount of data that new sensor-based technologies nowadays provide. Among the measurement modes that these sensors can obtain, there are also distributional scale data such as, grain size or particle size distributions. This information is of crucial importance in order to relate upstream deposit information with downstream processing processes. Data assimilation of distributional variables still presents several challenges. For instance, an adaptation of the classical formulation of Kalman filtering needs to be extended to the general Bayes Hilbert Space. In this work, we apply the general theory of Bayes Hilbert spaces to develop a Kalman Filter method allowing for sequential data assimilation of distributional variables with infinite support. Two different sets of information with different variability are tested. These are particle size and grain size distribution. After validation, a sensitivity analysis is performed to investigate the effects of different parameters. Practical implementation aspects are also discussed to allow for an effective application within an operating mine.

Applied sciences have witnessed an explosion of georeferenced data. Object oriented spatial statistics (O2S2) is a recent system of ideas that provides a solid framework where the new challenges posed by the GeoData revolution can be faced, by grounding the analysis on a powerful geometrical and topological approach. We shall present a perspective on O2S2, as a fruitful ground where novel computational approaches to geosciences can be developed, at the very interface among varied fields of applied sciences – including mathematics, statistics, computer science and engineering.

Atrioventricular block in the young is a rare condition. It is defined as congenital when diagnosed in utero, at birth or during the first month of life.

We address the problem of stochastic simulation of soil particle-size curves (PSCs) in heterogeneous aquifer systems. Unlike traditional approaches that focus solely on a few selected features of PSCs (e.g., selected quantiles), our approach considers the entire particle-size curves and can optionally include conditioning on available data. We rely on our prior work to model PSCs as cumulative distribution functions and interpret their density functions as functional compositions. We thus approximate the latter through an expansion over an appropriate basis of functions. This enables us to (a) effectively deal with the data dimensionality and constraints and (b) to develop a simulation method for PSCs based upon a suitable and well defined projection procedure. The new theoretical framework allows representing and reproducing the complete information content embedded in PSC data. As a first field application, we demonstrate the quality of unconditional and conditional simulations obtained with our methodology by considering a set of particle-size curves collected within a shallow alluvial aquifer in the Neckar river valley, Germany.