Probabilistic study of well capture zones distribution at the Lauswiesen field site

Stoch Environ Res Risk Assess

Secchi

2014

We consider the problem of predicting the spatial field of particle-size curves (PSCs) from a sample observed at a finite set of locations within an alluvial aquifer near the city of Tübingen, Germany. We interpret PSCs as cumulative distribution functions and their derivatives as probability density functions. We thus (a) embed the available data into an infinite-dimensional Hilbert Space of compositional functions endowed with the Aitchison geometry and (b) develop new geostatistical methods for the analysis of spatially dependent functional compositional data. This approach enables one to provide predictions at unsampled locations for these types of data, which are commonly available in hydrogeological applications, together with a quantification of the associated uncertainty. The proposed functional compositional kriging (FCK) predictor is tested on a one-dimensional application relying on a set of 60 PSCs collected along a 5-m deep borehole at the test site. The quality of FCK predictions of PSCs is evaluated through leave-one-out cross-validation on the available data, smoothed by means of Bernstein Polynomials. A comparison of estimates of hydraulic conductivity obtained via our FCK approach against those rendered by classical kriging of effective particle diameters (i.e., quantiles of the PSCs) is provided. Unlike traditional approaches, our method fully exploits the functional form of PSCs and enables one to project the complete information content embedded in the PSC to unsampled locations in the system.

Section: Field Datamentioning

confidence: 99%

Section: Field Datamentioning

confidence: 99%

Section: Field Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A kriging approach based on Aitchison geometry for the characterization of particle-size curves in heterogeneous aquifers

Menafoglio

Stoch Environ Res Risk Assess

Secchi

2014

Estimation of spatial covariance of log conductivity from particle size data

Riva

Sánchez-Vila²,

Water Resources Research

2014

We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and porosity. The latter quantities can be directly measured during routine sedimentological analyses of soil samples and provide a way of incorporating K estimates into groundwater flow models at a relatively modest experimental cost. Here we rely on widely used empirical formulations requiring measurements of representative particle diameters and, in some cases, of medium porosity. We derive exact formulations relating the spatial covariance of these quantities and K and present workable approximations on the basis of perturbation methods. Our formulations provide a direct link between key geostatistical descriptors of sedimentological and hydraulic parameters of heterogeneous aquifers which can be employed in classical estimation and simulation procedures. The approach and theoretical results are tested on an extensive data set comprising 411 particle size curves collected at 12 boreholes in a small-scale alluvial aquifer.

Stochastic simulation of soil particle‐size curves in heterogeneous aquifer systems through a Bayes space approach

Menafoglio

Water Resources Research

Secchi

2016

Self Cite

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