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Section: Research Program
Methodological developments
In addition to the application-driven sections, the team will also work on the following theoretical questions. They are clearly connected to the abovementioned scientific issues but do not correspond to a specific application or process.
Stochastic models for extreme events
State of the Art
Max-stable random fields [67], [65], [52], [32], [59] are the natural limit models for spatial maximum data and have spawned a very rich literature. An overview of typical approaches to modelling maxima is due to [34]. Physical interpretation of simulated data from such models can be discussed. An alternative to the max-stable framework are models for threshold exceedances. Processes called GPD processes, which appears as a generalization of the univariate formalism of the high thresholds exceeding a threshold based on the GPD, have been proposed [39], [71]. Strong advantages of these thresholding techniques are their capability to exploit more information from the data and explicitly model the original event data. However, the asymptotic dependence stability in these limiting processes for maximum and threshold exceedance tends to be overly restrictive when asymptotic dependence strength decreases at high levels and may ultimately vanish in the case of asymptotic independence. Such behaviours appear to be characteristic for many real-world data sets such as precipitation fields [33], [70]. This has motivated the development of more flexible dependence models such as max-mixtures of max-stable and asymptotically independent processes [76], [20] for maxima data, and Gaussian scale mixture processes [60], [51] for threshold exceedances. These models can accommodate asymptotic dependence, asymptotic independence and Gaussian dependence with a smooth transition. Extreme events also generally present a temporal dependence [73] . Developing flexible space-time models for extremes is crucial for characterizing the temporal persistence of extreme events spanning several time steps; such models are important for short-term prediction in applications such as the forecasting of wind power and for extreme event scenario generators providing inputs to impact models, for instance in hydrology and agriculture. Currently, only few models are available from the statistical literature (see for instance [30], [31], [50]) and remain difficult to interpret.
Four year research objectives
The objective is to extend state-of-the-art methodology with respect to three important aspects: 1) adapting well-studied spatial modelling techniques for extreme events based on asymptotically justified models for threshold exceedances to the space-time setup; 2) replacing restrictive parametric dependence modelling by semiparametric or nonparametric approaches; 3) proposing more flexible spatial models in terms of asymmetry or in terms of dependence. This means being able to capture the strength of potentially decreasing extremal dependence when moving towards higher values, which requires developing models that allow for so-called asymptotic independence.
People
Gwladys TOULEMONDE , Fátima Palacios Rodríguez
External collaborations
In a natural way, the Cerise project members are the main collaborators for developing and studying new stochastic models for extremes.
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More specifically, research with Jean-Noel Bacro (IMAG, UM), Carlo Gaetan (DAIS, Italy) and Thomas Opitz (BioSP, MIA, INRA) focuses on relaxing dependence hypothesis.
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The asymmetry issue and generalization of some Copula-based models are studied with Julie Carreau (IRD, HydroSciences, UM).
Integrating heterogeneous data
State of the Art
Assuming that a given hydrodynamic models is deemed to perform satisfactorily, this is far from being sufficient for its practical application. Accurate information is required concerning the overall geometry of the area under study and model parametrization is a necessary step towards the operational use. When large areas are considered, data acquisition may turn out prohibitive in terms of cost and time, not to mention the fact that information is sometimes not accessible directly on the field. To give but one example, how can the roughness of an underground sewer pipe be measured?
A strategy should be established to benefit from all the possible sources of information in order to gather data into a geographical database, along with confidence indexes.
Four year research objectives
The assumption is made that even hardly accessible information often exists. This stems from the increasing availability of remote-sensing data, to the crowdsourcing of geographical databases, including the inexhaustible source of information provided by the internet. However, information remains quite fragmented and stored in various formats: images, vector shapes, texts, etc. The overall objective of this research line is to develop methodologies to gather various types of data in the aim of producing an accurate mapping of the studied systems for hydrodynamics models.
One possible application concerns the combination of on-field elevation measurements and level lines extracted from remote sensing data in the aim of retrieving the general topography of the domain (see section 3.1.4).
Another application studied in the Cart'Eaux project, is the production of regular and complete mapping of urban sewer systems. Contrary to drinkable water networks, the knowledge of sewer pipe location is not straightforward, even in developed countries. The methodology applied consists in inferring the shape of the network from a partial dataset of manhole covers that can be detected from aerial images [61]. Since manhole covers positions are expected to be known with low accuracy (positional uncertainty, detection errors), a stochastic algorithm will be set up to provide a set of probable network geometries. As more information is required for hydraulic modelling than the simple mapping of the network (slopes, diameters, materials, etc.), text data mining is used to extract characteristics from data posted on the Web or available through governmental or specific databases. Using an appropriate keyword list, the web is scanned for text documents. Thematic entities are identified and linked to the surrounding spatial and temporal entities in order to ease the burden of data collection. It is clear at this stage that obtaining numerical values on specific pipes will be challenging. Thus, when no information is found, decision rules will be used to assign acceptable numerical values to enable the final hydraulic modelling.
In any case, the confidence associated to each piece of data, be it directly measured or reached from a roundabout route, should be assessed and taken into account in the modelling process. This can be done by generating a set of probable inputs (geometry, boundary conditions, forcing, etc.) yielding simulation results along with the associated uncertainty.
People
Carole DELENNE , Vincent GUINOT , Gwladys TOULEMONDE , Benjamin Commandré
External collaborations
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The Cart'Eaux project has been a lever to develop a collaboration with Berger-Levrault company and several multidisciplinary collaborations for image treatment (LIRMM), text analysis (LIRMM and TETIS) and network cartography (LISAH, IFSTTAR). These collaborations will continue with the submission of new projects.
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The problematic of inferring a connected network from scarce or uncertain data is common to several research topics in LEMON such as sewage or drainage systems, urban media and wetlands. A generic methodology will be developed in collaboration with J.-S. Bailly (LISAH).
Numerical methods for porosity models
State of the Art
Porosity-based shallow water models are governed by hyperbolic systems of conservation laws. The most widespread method used to solve such systems is the finite volume approach. The fluxes are computed by solving Riemann problems at the cell interfaces. This requires that the wave propagation properties stemming from the governing equations be known with sufficient accuracy. Most porosity models, however, are governed by non-standard hyperbolic systems.
Firstly, the most recently developed DIP models include a momentum source term involving the divergence of the momentum fluxes [6]. This source term is not active in all situations but takes effect only when positive waves are involved [46] [4]. The consequence is a discontinuous flux tensor and discontinuous wave propagation properties. The consequences of this on the existence and uniqueness of solutions to initial value problems (especially the Riemann problem) are not known. Nor are the consequences on the accuracy of the numerical methods used to solve this new type of equations.
Secondly, most applications of these models involve anisotropic porosity fields [53], [64]. Such anisotropy can be modelled using porosity tensors, with principal directions that are not aligned with those of the Riemann problems in two dimensions of space. The solution of such Riemann problems has not been investigated yet. Moreover, the governing equations not being invariant by rotation, their solution on unstructured grids is not straightforward.
Thirdly, the Riemann-based, finite volume solution of the governing equations require that the Riemann problem be solved in the presence of a porosity discontinuity. While recent work [38] has addressed the issue for the single porosity equations, similar work remains to be done for integral- and multiple porosity-based models.
Four year research objectives
The four year research objectives are the following:
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investigate the properties of the analytical solutions of the Riemann problem for a continuous, anisotropic porosity field,
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extend the properties of such analytical solutions to discontinuous porosity fields,
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derive accurate and CPU-efficient approximate Riemann solvers for the solution of the conservation form of the porosity equations.
People
Vincent GUINOT , Antoine ROUSSEAU
External collaborations
Owing to the limited staff of the Lemon team, external collaborations will be sought with researchers in applied mathematics. Examples of researchers working in the field are
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