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Mathematical Hydrogeology: from characterization to forecasts

Applicant Renard Philippe
Number 124979
Funding scheme SNSF Professorships
Research institution Centre d'hydrogéologie et de géothermie Université de Neuchâtel
Institution of higher education University of Neuchatel - NE
Main discipline Other disciplines of Earth Sciences
Start/End 01.10.2009 - 28.02.2011
Approved amount 255'626.00
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Keywords (9)

Hydrogéologie; Incertitude; Hétérogénéité; Géostatistique; Aquifer characterization; geostatistics; multiple-point statistics; alluvial aquifer; probability aggregation

Lay Summary (English)

Lay summary
LeadOften geological knowledge is not accounted for as much as it should when constructing stochastic aquifer models. This project aims at improving the integration of geology in mathematical hydrogeology by developing new mathematical techniques and the corresponding computer codes.SummaryMulti-Gaussian statistical techniques that are currently used to model geological heterogeneity do not allow to integrate conceptual geological knowledge and systematically impose that high permeability or low permeability areas are disconnected. This has a tremendous impact on groundwater flow and transport models. Among the possible alternative statistical methods, multiple-points statistics is one of the most general. In this project, we will pursue our research on the development of multiple-point statistics tools and theories by focusing on techniques allowing to widen the range of application of the method and better control its performances and statistical significance. This will provide a general framework for the integration of geological knowledge during hydrogeological site characterization.AimThe aim of the project is to facilitate the application of multiple-point statistics. More precisely, we will work on probability aggregation techniques and investigate their performances for the simulation of aquifer structures in an alluvial environment in 3D with multiple-point statistics based on 2D training images. In addition, we will analyze how the parameters of the multiple-point statistics can be inferred from field observations and how they control the forecasted uncertainty.SignificanceMultiple-point statistics may have a very wide range of applications since they are applicable to any type of variables. While they have mainly be developed for the simulation of geological heterogeneity, it is rather straightforward to apply the same techniques in other fields. For example, time series simulation can be conducted in a simple manner with the method. The advantage of the proposed technique is that it requires only a few parameters to model a complex structure either in space or in time. This can be used for interpolation, extrapolation, reconstruction of missing data, or pure simulation for risk analysis.
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants


Associated projects

Number Title Start Funding scheme
106557 Mathematical hydrogeology: from characterization to forecasts 01.10.2005 SNSF Professorships
182600 Phenix - Alternative stochastic models for data integration and robust uncertainty quantification in hydrogeology 01.02.2019 Project funding


The proposed project is the continuation of the project entitled “Mathematical hydrogeology: from characterization to forecast”. Its general aim is to provide new mathematical tools and the corresponding computer codes to facilitate 1) aquifer characterization and 2) evaluation of uncertainties. More precisely, the aim is to propose a set of tools allowing to take into account the available geological knowledge on a site and to integrate it with all the available sources of information (direct geological observations, measurements of state variables such as piezometric heads, water temperatures, chemistry, etc, and indirect observations such as geophysics). The motivation for developing such methods is based on two observations: 1) geology is often not accounted for in the existing methods while this knowledge is available and crucial for understanding the internal architecture and the connectivity of the reservoirs, 2) there is often a large amount of data, collected at a great cost, which is not interpreted in a rigorous manner.More precisely, the multi-Gaussian statistical techniques that are currently used to model heterogeneity are not sufficient because they impose implicitly the connectivity of intermediate values. This feature of the multi-Gaussian model influences strongly flow and transport simulations in underground reservoirs and can lead to inadequate forecasts. Alternative statistical methods are needed to better model the connectivity and to account for the available geological knowledge. The proposed research is therefore focused on multiple-points statistics which is the most flexible technique at the moment. It can account for the geological knowledge and from indirect observations such as geophysics. However, the model must also be constrained by available hydrogeological observations (heads, concentrations, etc.). To this end, multiple-point statistics must be coupled with inverse methods. In a broad sense, inverse methods are extremely important because they are the basic quantitative method to analyze and interpret field observations with the help of models. Last but not least, tools are also required to propagate uncertainty in the most general and efficient fashion in order to evaluate the impact of imperfect knowledge and uncertainty on forecasts. This is why the project is still organized in 4 inter-related topics: connectivity, multiple-point simulation techniques, inverse problem, and uncertainty propagation.The new project is based on the results that have been obtained so far and proposes to consolidate or to extend them. Among these results, the direct sampling multiple point approach is extremely appealing and promising. It provides solutions to most of the limitations of existing multiple-point statistics techniques. One of the most important improvements is that it allows to work with continuous variables and not only with categorical variables. A PhD thesis on this topic will be defended in September 2009. Another important result is the moving window inverse technique. It is based on a Monte Carlo Markov Chain approach and the preliminary results are promising. Because the direct sampling multiple-point approach is completely new, it has not yet been fully tested and has not yet been integrated in the moving window algorithm. One of the aims of the new project is therefore to integrate the new multiple-point method in the inverse technique. We propose to test two approaches to make that coupling. One consists in consolidating the moving window algorithm by replacing the old multiple point algorithm by the new one. The second approach consists in combining the regularized pilot point method with the new direct sampling algorithm which is capable of handling continuous variables. A new topic that we propose to investigate is the use of importance sampling to accelerate the convergence of Monte Carlo analysis both for the inverse and direct problem.