Scale effect in hazard assessment - application to daily rainfall

International audienceDaily precipitation is recorded as the total amount of water collected by a rain-gauge in 24h. Events are modelled as a Poisson process and the 24h precipitation by a Generalized Pareto Distribution (GPD) of excesses. Hazard assessment is complete when estimates of the Poisson rate and the distribution parameters, together with a measure of their uncertainty, are obtained. The shape parameter of the GPD determines the support of the variable: Weibull domain of attraction (DA) corresponds to finite support variables, as should be for natural phenomena. However, Fréchet DA has been reported for daily precipitation, which implies an infinite support and a heavy-tailed distribution. We use the fact that a log-scale is better suited to the type of variable analyzed to overcome this inconsistency, thus showing that using the appropriate natural scale can be extremely important for proper hazard assessment. The approach is illustrated with precipitation data from the Eastern coast of the Iberian Peninsula affected by severe convective precipitation. The estimation is carried out by using Bayesian techniques

Biplots for compositional data derived from generalized joint diagonalization methods

Biplots constructed from principal components of a compositional data set are an established means to explore its features. Principal Component Analysis (PCA) is also used to transform a set of spatial variables into spatially decorrelated factors. However, because no spatial structures are accounted for in the transformation the application of PCA is limited. In geostatistics and blind source separation a variety of different matrix diagonalization methods have been developed with the aim to provide spatially or temporally decorrelated factors. Just as PCA, many of these transformations are linear and so lend themselves to the construction of biplots. In this contribution we consider such biplots for a number of methods (MAF, UWEDGE and RJD transformations) and discuss how and if they can contribute to our understanding of relationships between the components of regionalized compositions. A comparison of the biplots with the PCA biplot commonly used in compositional data analysis for the case of data from the Northern Irish geochemical survey shows that the biplots from MAF and UWEDGE are comparable as are those from PCA and RJD. The biplots emphasize different aspects of the regionalized composition: for MAF and UWEDGE the focus is the spatial continuity, while for PCA and RJD it is variance explained. The results indicate that PCA and MAF combined provide adequate and complementary means for exploratory statistical analysis

The effect of scale in daily precipitation hazard assessment

Daily precipitation is recorded as the total amount of water collected by a rain-gauge in 24 h. Events are modelled as a Poisson process and the 24 h precipitation by a Generalised Pareto Distribution (GPD) of excesses. Hazard assessment is complete when estimates of the Poisson rate and the distribution parameters, together with a measure of their uncertainty, are obtained. The shape parameter of the GPD determines the support of the variable: Weibull domain of attraction (DA) corresponds to finite support variables as should be for natural phenomena. However, Fréchet DA has been reported for daily precipitation, which implies an infinite support and a heavy-tailed distribution. Bayesian techniques are used to estimate the parameters. The approach is illustrated with precipitation data from the Eastern coast of the Iberian Peninsula affected by severe convective precipitation. The estimated GPD is mainly in the Fréchet DA, something incompatible with the common sense assumption of that precipitation is a bounded phenomenon. The bounded character of precipitation is then taken as a priori hypothesis. Consistency of this hypothesis with the data is checked in two cases: using the raw-data (in mm) and using log-transformed data. As expected, a Bayesian model checking clearly rejects the model in the raw-data case. However, log-transformed data seem to be consistent with the model. This fact may be due to the adequacy of the log-scale to represent positive measurements for which differences are better relative than absolute

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

Improving processing by adaption to conditional geostatistical simulation of block compositions

Exploitation of an ore deposit can be optimized by adapting the beneficiation processes to the properties of individual ore blocks. This can involve switching in and out certain treatment steps, or setting their controlling parameters. Optimizing this set of decisions requires the full conditional distribution of all relevant physical parameters and chemical attributes of the feed, including concentration of value elements and abundance of penalty elements. As a first step towards adaptive processing, the mapping of adaptive decisions is explored based on the composition, in value and penalty elements, of the selective mining units. Conditional distributions at block support are derived from cokriging and geostatistical simulation of log-ratios. A one-to-one log-ratio transformation is applied to the data, followed by modelling via classical multivariate geostatistical tools, and subsequent back-transforming of predictions and simulations. Back-transformed point-support simulations can then be averaged to obtain block averages that are fed into the process chain model. The approach is illustrated with a \u27toy\u27 example where a four-component system (a value element, two penalty elements, and some liberable material) is beneficiated through a chain of technical processes. The results show that a gain function based on full distributions outperforms the more traditional approach of using unbiased estimates

Interpolation algorithm ranking using cross-validation and the role of smoothing effect. A coal zone example

For a property measured at several locations, interpolation algorithms provide a unique and smooth function yielding a locally realistic estimation at any point within the sampled region. Previous studies searching for optimal interpolation strategies by measuring cross-validation error have not found consistent rankings; this fact was traditionally explained by differences in the distribution, spatial variability and sampling patterns of the datasets. This article demonstrates that ranking differences are also related to interpolation smoothing, an important factor controlling cross-validation errors that was not considered previously. Indeed, smoothing in average-based interpolation algorithms depends on the number of neighbouring data points used to obtain each interpolated value, among other algorithm parameters. A 3D dataset of calorific value measurements from a coal zone is used to demonstrate that different algorithm rankings can be obtained solely by varying the number of neighbouring points considered (i.e. whilst maintaining the distribution, spatial variability and sampling pattern of the dataset). These results suggest that cross-validation error cannot be used as a unique criterion to compare the performance of interpolation algorithms, as has been done in the past, and indicate that smoothing should be also 26 coupled to search for optimum and geologically realistic interpolation algorithms

Towards geostatistical learning for the geosciences: A case study in improving the spatial awareness of spectral clustering

The particularities of geosystems and geoscience data must be understood before any development or implementation of statistical learning algorithms. Without such knowledge, the predictions and inferences may not be accurate and physically consistent. Accuracy, transparency and interpretability, credibility, and physical realism are minimum criteria for statistical learning algorithms when applied to the geosciences. This study briefly reviews several characteristics of geoscience data and challenges for novel statistical learning algorithms. A novel spatial spectral clustering approach is introduced to illustrate how statistical learners can be adapted for modelling geoscience data. The spatial awareness and physical realism of the spectral clustering are improved by utilising a dissimilarity matrix based on nonparametric higher-order spatial statistics. The proposed model-free technique can identify meaningful spatial clusters (i.e. meaningful geographical subregions) from multivariate spatial data at different scales without the need to define a model of co-dependence. Several mixed (e.g. continuous and categorical) variables can be used as inputs to the proposed clustering technique. The proposed technique is illustrated using synthetic and real mining datasets. The results of the case studies confirm the usefulness of the proposed method for modelling spatial data

Garnet major‑element composition as an indicator of host‑rock type: a machine learning approach using the random forest classifier

The major-element chemical composition of garnet provides valuable petrogenetic information, particularly in metamorphic rocks. When facing detrital garnet, information about the bulk-rock composition and mineral paragenesis of the initial garnet-bearing host-rock is absent. This prevents the application of chemical thermo-barometric techniques and calls for quantitative empirical approaches. Here we present a garnet host-rock discrimination scheme that is based on a random forest machine-learning algorithm trained on a large dataset of 13,615 chemical analyses of garnet that covers a wide variety of garnet-bearing lithologies. Considering the out-of-bag error, the scheme correctly predicts the original garnet host-rock in (i) > 95% concerning the setting, that is either mantle, metamorphic, igneous, or metasomatic; (ii) > 84% concerning the metamorphic facies, that is either blueschist/greenschist, amphibolite, granulite, or eclogite/ultrahigh-pressure; and (iii) > 93% concerning the host-rock bulk composition, that is either intermediate–felsic/metasedimentary, mafic, ultramafic, alkaline, or calc–silicate. The wide coverage of potential host rocks, the detailed prediction classes, the high discrimination rates, and the successfully tested real-case applications demonstrate that the introduced scheme overcomes many issues related to previous schemes. This highlights the potential of transferring the applied discrimination strategy to the broad range of detrital minerals beyond garnet. For easy and quick usage, a freely accessible web app is provided that guides the user in five steps from garnet composition to prediction results including data visualization

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