Emulation techniques for the REduction, Sensitivity Analysis and INversion of models for subsurface hydrology – RESAIN

Analytical and numerical development for efficient Global sensitivty Analysis and uncertainty analysis
Application to flow and transport in the karstified aquifer of the Hydrogeological Experimental Site (HES) in Poitiers
Application to modeling reactive transport in the presence of biofilms at the laboratory scale.

develepment of a rigourous method for assessing influent parameters controling tranfers in natural porous media. Analysis of paremeter uncertainty on model results
decomposition of a spatially distributed paremeter field by the Karouen-Loeve method

Application to both syntheteic problems and data from concrete case studies

Publications of results in reputable scientific journals will be an essential task of the project.

Underground systems remain often poorly known as regard flow and transport. The main reason is the under-sampled nature of underground reservoirs with the meaning that observations are limited to a few wells compared with the several km3 of host rocks. Even though the last two decades revealed fruitful to ground water modeling, the question of model inversion is still teasing. To make it short, pinpoint fitting of a model onto scarce data never ensures that the model is predictive: 1- several solutions may exist to the same problem, 2- the model sensitivity to parameters is usually "local", i.e., calculated in the close vicinity of an optimal solution. What if this solution is wrong and the behavior of the system ignored for a wide range of reasonably acceptable parameters?
A recent example grounded on intensive studies of the limestone aquifer at the Hydrogeological Experimental Site - Poitiers (HES – National Observatory Tasks appointed by CNRS – France) showed that complex channeled flow and transport could be approached by several mechanistic models. Automatic inversions of these models pointed out that a local sensitivity analysis was unable to distinguish solutions with physical meaning from that with awkward parameter values. Notably, several conceptualizations of flow and transport also returned solutions for which the modeler was unable to rank one as better than the other.
Thus, there is a crux need for handling uncertainty/sensitivity analysis and inverse problems differently. The RESAIN project is aimed at developing a methodology to address these topics in a "global" manner for both complex flow and transport conditioned onto real data, presently that from the HES-Poitiers. The global analysis is assumed to inform on the model behavior for wide ranges of parameter values and is a priori disconnected from any specific fitting of a given problem.
This analysis will be based on meta-models, i.e., surrogates of the initial model with the same physical-numerical behavior and the same parameterization but easier to compute. These meta-models will be inferred as Polynomial Chaos Expansions (PCE) allowing the influence of a single parameter, or any n-uplet to be lumped onto pre-fixed bases of orthogonal polynomials. The PCE can be performed following either the so-called non-intrusive or intrusive methods. The non intrusive form is based on a Monte-Carlo training of the PCE over equiprobable realizations of the initial model while making to vary the parameters over wide ranges. The Intrusive form embeds the polynomial forms directly into the partial differential equations representing the model. Both approaches will be undertaken for both deterministic and stochastic parameterizations. The stochastic parameterization of a spatially distributed model will be handled by the Karhunen-Loève decomposition. The latter allows replacing a cumbersome parameterization (e.g., a random value at each cell discritizing the Euclidean space) by a vector of scalars of limited size. All meta-models will be trained on initial models that proved their worth for complex flow and transport. These models are based on dual-continua that can be degraded at will according to the prevailing mechanisms. By comparing sensitivity/uncertainty analysis between PCE's of these different models, the conditions making a mechanism dominant will be assessed as well as the potential information on this mechanism enclosed in data. Then, a series of meta-model inversions will be performed on the HES data. It is expected that the good knowledge of the model and its global sensitivity will speed up the inversion procedure and moderate wanderings in the parameter space by seeking unphysical solutions. Because the initial models are general and versatile, it is obvious that RESAIN will yield a methodology not only applicable to the specific case of the HES but also affordable and applicable to much wider contexts.