Mise en oeuvre du krigeage sur arbre.

International audienceUn modèle de fonctions aléatoires définies sur une topologie d'arbre (de Fouquet & Bernard-Michel, 2006) a été développé pour l'estimation de concentrations le long d'un réseau hydrographique. Le principe consiste à décomposer le réseau en filets élémentaires joignant chaque " source " à " l'exutoire ". La concentration Z au point x s'exprime comme une combinaison linéaire Z(x)=\Sum wiYi(x) de variables aléatoires élémentaires Yi définies sur ces filets, dont les coefficients wi dépendent de la position sur l'arbre. Le krigeage des concentrations au point x revient donc à l'estimation d'une combinaison linéaire des Yi(x) à partir d'autres combinaisons linéaires, les concentrations mesurées aux points expérimentaux $x_\alpha$; : Z(x_\alpha)= \Sum wi(x_\alpha)Yi(x_\alpha). Le krigeage dépend des hypothèses sur les concentrations, qui se ramènent à des hypothèses sur les variables élémentaires Yi et sur les coefficients wi. Ces hypothèses déterminent les conditions requises pour l'estimation : le nombre minimum de mesures et leur répartition par arête. Ce modèle est appliqué aux concentrations en nitrates sur un réseau constitué d'une petite portion de la Seine (de l'amont de Paris à l'estuaire) et de la Marne. Tout d'abord, la simulation déterministe ProSe, disponible en tout point (Even et al., 1998), permet de tester les hypothèses. Ensuite, le krigeage est effectué à partir des mesures aux stations effectivement disponibles

Historical energy price shocks and their changing effects on the economy

The purpose of this paper is to identify the changes in the impact of energy shocks on economic activity – with an interest in assessing if an economy's vulnerability and resilience to shocks improved with economic development. Using data on the United Kingdom over the last three hundred years, the paper identifies supply, aggregate demand and residual shocks to energy prices and estimates their changing influence on energy prices and GDP. The results suggest that the impacts of supply shocks rose with its increasing dependence on coal, and declined with its partial transition to oil. However, the transition from exporting coal to importing oil increased the negative impacts of demand shocks. More generally, the results indicate that improvements in vulnerability and resilience to shocks did not progress systematically as the economy developed. Instead, the changes in impacts depended greatly on the circumstances related to the demand for and supply of energy sources. If these experiences are transferable to future markets, a transition to renewable energy sources is likely to reduce vulnerability and increase resilience to energy price shocks

Optimal spatial design for air quality measurement surveys: what criteria?

International audienceIn this work, we present a spatial statistical methodology to design benzene air concentration measurement surveys at the urban scale. In a first step, we define an a priori modeling based on an analysis of data coming from previous campaigns on two different agglomerations. More precisely, we retain a modeling with an external drift which consists of a drift plus a spatially correlated residual. The statistical analysis performed leads us to choose the most relevant auxiliary variables and to determine an a priori variogram model for the residual. An a priori distribution is also defined for the variogram parameters, whose values appear to vary from a campaign to another. In a second step, we optimize the positioning of the measuring devices on a third agglomeration according to a Bayesian criterion. Practically, we aim at finding the design that minimizes the mean over the urban domain of the universal kriging variance, whose parameters are based on the a priori modeling, while accounting for the prior distribution over the variogram parameters. Two optimization algorithms are then compared: simulated annealing and a particle filter based algorithm

Influence of geological parameters on CO2 storage prediction in deep saline aquifer at industrial scale

International audienceConsequences of uncertainties on geological parameters are examined using 2D models at large extension. Reduction of the uncertainties on predictions is also investigated, either because parameter's influence is negligible for the project design, or by showing for which parameters additional data will significantly increase the quality of prediction. TOUGH2/ECO2N is used to simulate the injection of millions tonnes of CO2 for the specific case of the Dogger aquifer (carbonates aquifer in the Paris Basin) with high lateral and vertical heterogeneities and for which few data are available. Studied parameters are spatial variability and correlation length of permeability, value of absolute permeability, pore compressibility, caprock permeability and relative permeability curves. Several numerical models of permeability are constructed: two uniform cases (two values of permeability) and 200 geostatistical initial realizations, which are modified according to the studied parameters. Results are compared in terms of propagation of pressure perturbations, injectivity (pressure in the vicinity of the well) and in terms of gas migration and dissolution. The results indicate, for the specific scale and values, that: (1) Pore compressibility, absolute value and spatial variability of permeability have the main influence on pressure propagation and injectivity. Relative permeability curves and correlation lengths have a weaker influence for the peak of pressure but tend to increase the variations for maximum/minimum cases. (2) Relative permeability curves and heterogeneities have a significant impact on prediction of gas dissolution and migration. At last, we also investigate the possibility to reduce the number of runs

The influence of spatial variability on 2D reactive transport simulations

International audienceIn reactive transport simulations, the effects of the spatial variability of geological media are generally neglected. The impact of this variability is systematically examined here in 2D simulations, with a simple geometry and chemistry with a positive feedback: increase of porosity and of permeability during calcite dissolution. The results highlight the leading role in these conditions of: (i) the correlation length of porosity and of permeability; and (ii) the kinematic dispersivity, whose effects are dominant compared to those of variance and reaction kinetics. The impact of stochastic variability (between several randomdraws) is also significant, as it is of the same order of magnitude as the impact of the range and dispersivity

Equivalent block transmissivity in an irregular 2D polygonal grid for one-phase flow: a sensitivity analysis

International audienceUpscaling is needed to transform the representation of non additive space-dependent variables, such as permeability, from the fine grid of geostatistical simulations (to simulate small scale spatial variability) to the coarser, generally irregular grids for hydrodynamic transport codes. A new renormalisation method is proposed, based on the geometric properties of a Voronoï grid. It is compared to other classic methods by a sensitivity analysis (grid, range and sill of the variogram, random realisation of a simulation); the criterion is the flux of a tracer at the outlet. The effect of the upscaling technique on the results appears to be of second order compared to the spatial discretisation, the choice of variogram, and the realisation

Caractérisation spatiale et temporelle des "Masses d'Eau Cours d'Eau". Spatial and Temporal characterization of "River Water Bodies".

International audienceThis article aims to understand how to extrapolate in space and time discrete measurements in order to calculate physico-chemical indicators in rivers, which are required by the Water Framework Directive. Linked to this issue, few questions are addressed. Does the French National Basin Network provide enough information in order to make consistent water quality maps? How does the temporal indicator - the 90 percentile - vary in space? The outputs of the ProSe model applied to the Seine River are used to compare two different methods for calculating the 90 percentile: the classical method based on the empirical percentile function and a method that aims to reduce the estimation bias of the 90 percentile. This second method includes temporal weighting and linearization o the empirical percentile function, and therefore its application is a little more complex. But with this method the bias induced by irregular and/or few measurements is reduced. Three methods for spatializing the 90 percentiles have been tested in order to obtain occurrence percentages of the percentiles for each quality class. The first one is based on the "failure principle" and consists in keeping only the worst site for the considered "River Water Body". The second one respects the proportion of percentiles located in each quality class, while the third one allocates an influence segment to each measurement site. Spatializing temporal percentiles in "River Water Bodies" by influence segments leads to a marked improvement of occurrence percentage estimations and reveals the necessity to take into account the spatial configuration of measurement sites when calculating a quality indicator

Apport croisé de la modélisation déterministe et géostatistique. Exemple des concentrations en nitrates de la Seine.

5pages+résuméLe long des réseaux hydrographiques, l'espacement des stations de mesure des concentrations et l' hétérogénéité des mesures compliquent le calage des modèles géostatistiques nécessaires à l'estimation des concentrations (Bernard-Michel et de Fouquet, 2006). Le recours à un modèle déterministe peut-il permettre de remédier à la rareté des mesures, en fournissant débit, concentrations sur tout le domaine simulé ? Nous examinons par bief les résultats du modèle PROSE qui décrit la Seine et la Marne peu avant leur confluence jusqu'à Poses. Temporellement les mesures et la simulation PROSE sont ajustables en modèle linéaire de corégionalisation. Spatialement, le cokrigeage permet de recaler les conditions aux limites, et donc la simulation, aux mesures de contrôle. reproduisant la variabilité spatiale, mais faiblement corrélé aux mesures, le modèle PROSE s'interprète alors en terme de simulation non conditionnelle. Enfin, un modèle de variogramme tri-variable débit-flux-concentrations est ajusté spatialement

Spatial representativeness of an air quality monitoring station. Application to NO2 in urban areas

International audienceThe present study aims at setting up a geostatistical methodology that could be implemented in an operational context to assess the spatial representativeness of a measurement station. In the proposed definition, a point is considered as belonging to the area of representativeness of a station if its concentration differs from the station measurement by less than a given threshold. Additional criteria related to distance or environmental characteristics may also be introduced. Concentrations are first estimated at each point of the domain applying kriging techniques to passive sampling data obtained from measurement surveys. The standard deviation of the estimation error is then used, making a hypothesis on the error distribution, to select the points, at a fixed risk, where the difference of concentration with respect to the station is below the threshold. The methodology is then applied to NO2 experimental datasets for different French cities