Raimon Tolosana-Delgado

Assessing wavestorm hazard evolution in the NW Mediterranean with hindcast and buoy data

It has been suggested that climate change might modify the occurrence rate of large storms and their magnitude, due to a higher availability of energy in the atmosphere-ocean system. Forecasting physical models are commonly used to assess the effects. No one expects the physical model forecasts for one specific day to be accurate; we consider them to be good if they adequately describe the statistical characteristics of the climate. The Peak-Over-Threshold (POT) method is a common way to statistically treat the occurrence and magnitude of hazardous events: here, occurrence is modelled as a Poisson process and magnitude over a given threshold is assumed to follow a Generalized Pareto Distribution (GPD). We restrict our attention to Weibull-related GPDs, which exhibit an upper bound, to comply with the fact that any physical process has a finite upper limit. This contribution uses this framework to model time series of log-significant wave-height constructed joining quasi-collocated hindcast data and buoy measurements. Two of the POT model parameters (inhomogeneous Poisson rate and logarithm of the GPD shape parameter are considered to be a combination of a linear function of time and a series indicator function. The third parameter, logarithm of the GPD upper bound, is considered to have only a series indicator component. The resulting parameters are estimated using Bayesian methods. Using hincast and buoy series, the time span of the data set is extended, enhancing the precision of statistical results about potential linear changes. Simultaneously the statistical behaviour of hincast and buoy series are compared. At the same time, the step function allows to calibrate the statistical reproduction of storms by hindcasting.

An Affine Equivariant Multivariate Normal Score Transform for Compositional Data

The geostatistical treatment of continuous variables often includes a transformation to normal scores. In the case of analysing a composition, it has been suggested that standard methods can be applied to (isometric) logratio transformed compositions. Several logratio transformations are available and invariance of the final results under the choice of logratio transform is desirable. However, a geostatistical procedure which includes marginal normal scores transformations of the individual logratio scores via quantile matching will not have this invariance property, nor will the resulting vectors of scores show a joint multivariate normal distribution. In this paper an affine-equivariant normal score transform is proposed. The method is based on a continuous deformation of the underlying logratio space to a Gaussian space. The properties and performance of this method are illustrated and compared with existing alternatives using a simulated setting and a case study from a banded iron formation ore mining operation from Western Australia. The proposed method is also suitable for the study of other multivariate non-compositional cases.

Simplicial Indicator Kriging

Abstract Indicator kriging (IK) is a spatial interpolation technique devised for estimating a conditional cumulative distribution function at an unsampled location. The result is a discrete approximation, and its corresponding estimated probability density function can be viewed as a composition in the simplex. This fact suggested a compositional approach to IK which, by construction, avoids all its standard drawbacks (negative predictions, not-ordered or larger than one). Here, a simple algorithm to develop the procedure is presented.

Regression with compositional response having unobserved components or below detection limit values

The typical way to deal with zeros and missing values in compositional data sets is to impute them with a reasonable value, and then the desired statistical model is estimated with the imputed data set, e.g., a regression model. This contribution aims at presenting alternative approaches to this problem within the framework of Bayesian regression with a compositional response. In the first step, a compositional data set with missing data is considered to follow a normal distribution on the simplex, which mean value is given as an Aitchison affine linear combination of some fully observed explanatory variables. Both the coefficients of this linear combination and the missing values can be estimated with standard Gibbs sampling techniques. In the second step, a normally distributed additive error is considered superimposed on the compositional response, and values are taken as ‘below the detection limit’ (BDL) if they are ‘too small’ in comparison with the additive standard deviation of each variable. Within this framework, the regression parameters and all missing values (including BDL) can be estimated with a Metropolis-Hastings algorithm. Both methods estimate the regression coefficients without need of any preliminary imputation step, and adequately propagate the uncertainty derived from the fact that the missing values and BDL are not actually observed, something imputation methods cannot achieve.

Wave height data assimilation using non-stationary kriging

Data assimilation into numerical models should be both computationally fast and physically meaningful, in order to be applicable in online environmental surveillance. We present a way to improve assimilation for computationally intensive models, based on non-stationary kriging and a separable space-time covariance function. The method is illustrated with significant wave height data. The covariance function is expressed as a collection of fields: each one is obtained as the empirical covariance between the studied property (significant wave height in log-scale) at a pixel where a measurement is located (a wave-buoy is available) and the same parameter at every other pixel of the field. These covariances are computed from the available history of forecasts. The method provides a set of weights, that can be mapped for each measuring location, and that do not vary with time. Resulting weights may be used in a weighted average of the differences between the forecast and measured parameter. In the case presented, these weights may show long-range connection patterns, such as between the Catalan coast and the eastern coast of Sardinia, associated to common prevailing meteo-oceanographic conditions. When such patterns are considered as non-informative of the present situation, it is always possible to diminish their influence by relaxing the covariance maps.

A Truly Multivariate Normal Score Transform Based on Lagrangian Flow

In many geostatistical applications, a transformation to standard normality is a first step in order to apply standard algorithms in two-point geostatistics. However, in the case of a set of collocated variables, marginal normality of each variable does not imply multivariate normality of the set, and a joint transformation is required. In addition, current methods are not affine equivariant, as should be required for multivariate regionalized data sets without a unique, canonical representation (e.g., vector-valued random fields, compositional random fields, layer cake models). This contribution presents an affine equivariant method of Gaussian anamorphosis based on a flow deformation of the joint sample space of the variables. The method numerically solves the differential equation of a continuous flow deformation that would transform a kernel density estimate of the actual multivariate density of the data into a standard multivariate normal distribution. Properties of the flow anamorphosis are discussed for a synthetic application, and the implementation is illustrated via two data sets derived from Western Australian mining contexts.

Compositional Block Cokriging

Estimates of a whole block composition may be useful for improving the assessment and mining of resources, especially if the economic viability depends on more than just one metal or component. Banded Iron Formation (BIF) represents such a case, where optimal exploitation requires evaluation of Fe content, as well as waste and penalty elements. Block cokriging of the whole composition may yield these estimates. To avoid the spurious correlation problem, this should be based on log-ratios of the composition. But due to the non-linearity of the log-ratio transformations, this does not yield a direct change-of-support model. This contribution explores the approximation of this block average compositional cokriging by means of geostatistical simulation within the block. This methodology is illustrated with a BIF deposit of Western Australia.

Fundamental Concepts of Compositional Data Analysis

Compositional data is considered a statistical scale in its own right, with its own natural geometry and its own vector space structure. Compositional data analysis and this book cannot be understood without a basic knowledge of these issues and how they are represented in R. Therefore, this chapter introduces the basic geometric concepts of compositional data and of the R-package “compositions”: the relative nature of compositional data; how to load, represent, and display compositional data in R; the various compositional scales and geometries and how to select the right geometry for the problem at hand; and how to specify the geometry in “compositions” using the basic classes “acomp”, “rcomp”, “aplus”, “rplus”, “ccomp”, and “rplus”. A concise guide to the most important geometry for compositional data, the Aitchison geometry, is also included. The whole book relies on these basic principles, and the reader should make him or herself familiar with them in Sects. 2.1 – 2.5 before going on.

Process-based forward numerical ecological modeling for carbonate sedimentary basins

Nowadays, numerical modeling is a common tool used in the study of sedimentary basins, since it allows to quantify the processes simulated and to determine interactions among them. One of such programs is SIMSAFADIM-CLASTIC, a 3D forward-model process-based code to simulate the sedimentation in a marine basin at a geological time scale. It models the fluid flow, siliciclastic transport and sedimentation, and carbonate production. In this article, we present the last improvements in the carbonate production model, in particular about the usage of Generalized Lotka-Volterra equations that include logistic growth and interaction among species. Logistic growth is constrained by environmental parameters such as water depth, energy of the medium, and depositional profile. The environmental parameters are converted to factors and combined into one single environmental value to model the evolution of species. The interaction among species is quantified using the community matrix that captures the beneficial or detrimental effects of the presence of each species on the other. A theoretical example of a carbonate ramp is computed to show the interaction among carbonate and siliciclastic sediment, the effect of environmental parameters to the modeled species associations, and the interaction among these species associations. The distribution of the modeled species associations in the theoretical example presented is compared with the carbonate Oligocene-Miocene Asmari Formation in Iran and the Miocene Ragusa Platform in Italy.

Discriminant analysis of Palaeogene basalt lavas, Northern Ireland, using soil geochemistry

Palaeogene basalt lava (the Antrim Lava Group), extends over the north eastern corner of Northern Ireland and is composed of olivine tholeiite Lower and Upper Basalt formations that are separated by the Interbasaltic Formation. The latter represents a period of relative volcanic quiescence, and includes the quartz tholeiitic Causeway Tholeiitic Member in north County Antrim. As a result there are mineralogical and geochemical differences observed between the Basalt Formations. A comprehensive soil geochemical dataset from the Tellus Survey, Geological Survey Northern Ireland, provides a means to characterise the basalts. With this aim, we apply a discriminant analysis to this geochemical database. No relevant differences between the soils formed over the Lower and Upper Basalt formations are detected. The findings have significance for future investigation of potentially toxic elements present in the soils.